I would say that it is a bad idea to learn 'theory' without putting it into practise by playing an instrument. You can get all sorts of weird ideas and you will think of it analytically and mathematically and its not meant to be like that.
Theory has one useful purpose to me and that was learning to develop muscle memory. When I'm learning I usually start off slow and unsure so I have to count up notes, count triads, count inversions etc. My fingers are hesitant and I often hit the wrong notes or use the wrong fingers. After a while if you keep on drilling it the same way every day for half an hour to an hour over the course of a year your fingers become so used to falling into the right place that you begin to play on autopilot and you no longer need to count up notes. Your fingers just find the right keys. You need to learn proper and consistant fingering for this to work in your favour though. The most important thing is that your fingering is consistant.
A good analogy is learning how to type properly. The most efficient way is to start slow, keep the first 3 fingers on the left hand over the A S and D key and the first 3 fingers on the right hand over the J K and L keys. This way, every letter and things like space, tab and punctuation are all 1 key away. If you start learning like this and go it slow the idea is to develop a sort of muscle memory where after a while you no longer need to look at what keys you need to press when you type. If you find yourself reaching over several keys or moving your hands you should start over and take it slow again. Remember - consistancy is the most important thing to develop muscle memory that works.
It is exactly the same with piano and guitar and pretty much every instrument. The idea is to play it on feel but first you have to learn where everything is (whether it be letter keys or the notes of a scale) and you need to train your fingers to get used to going through the motions. Music theory helps to do that quickly and intuitively (especially for piano) but the idea is to eventually get to a point where you have no need of the theory anymore because it has become instinctive and second nature.
It is a difficult thing to describe but after 8 years of being an undisciplined guitar player and 1 year of being a disciplined keyboard player, I can say with much certainty that I don't think about what notes I am playing. I just sort of do it on autopilot. 8 years of messing up on guitar taught me many of the things that made me a better keyboard player in just a year. I am actually a very poor and uninspired guitar player considering how long I have been playing and this is mostly down to not being consistant and methodical in my learning. As such I have never been able to be deliver the goods consistantly with my first instrument and the range of feeling that I can express is limited by my rather poor technique.
The absolute worst
thing you can do is to learn theory for the sake of learning theory. It doesn't help you if you don't apply it to an instrument so that it becomes instinctive and reflexive. Never
ever get chord books that tell you what notes to press but don't tell you why you are pressing them or what fingers it is best to press them with. Theory is what you use to develop technique. If you have exceptional technique you can physically play anything and break it down with your fingers (not with your head). If you are learning theory I highly recommend you physically put it into practise by learning piano along with it. It is easy to see and hear and feel what you are doing which is important. Give it time and practise and you won't need to see or hear what you are doing - you can just play on the feel of it and this is a great place to be.
I must apologise if I sound like a cracked record but it is extremely important that your learning is logical and consistant. The best solution is to get a teacher who will keep you on track and nip any bad habits in the bud before they blossom into real problems but if you cannot afford one there are many good 'teach yourself piano/theory' resources online which will help you develop good consistant technique. There is a series of very good youtube videos by some young guy with crazy hair whose name I forget. Those lessons are actually good but what he doesn't elaborate on is that when he teaches you a new scale you don't just play it once and thats your learning done. You have to play it ascending, descending, left and right handed, both handed, cross handed and with your eyes closed. Then you have to keep on doing that slowly and as evenly as possible until you dont make any mistakes. Then you have to keep on doing that until you no longer need to look at or hear what you are doing. Then you need to play it faster. I recommend you check out those videos but I also recommend that you don't watch like 3 episodes a day. Only go on to the next episode when you have absolutely mastered everything he has taught you in those 6 or so minutes. It could take weeks or months before you go onto the next episode. It doesn't matter. Take it as slowly as you need to to develop your touch. Rushing it or getting ahead of yourself will harm you in the long run as it can lead to bad habits and sloppy technique. You will just be wasting your own time and it won't sink in.
What you don't want to do is learn the theory and not play an instrument or learn higher theory and not develop your technique to the point where you can actually play what you have learnt. If you do this, music theory will always be abstract and that is not a good thing. It should be intuitive and spontaneous. Theory can and does help you to get to a level where playing an instrument can be intuitive and spontaneous but you need to do it properly. But when you get to that level, you won't think about it anymore. You will just do it. This takes time, practise and discipline but if you are serious about it, it will save you time in the long run.
My 2 cents.
Edit: The crazy haired kid is called Lyper on youtube. His tutorial videos start here: YouTube - How to Play Piano: The basics, lesson #1
Edit 2: This is also a good resource to start learning the theoretical and practical side of playing piano: Free online piano lessons...learn piano scales, chords and more!
Obviously if you can afford a teacher and you are willing to put in the effort - go for it. Nothing beats face to face mentoring. For everyone else who can't get a scholarship and can't afford a personal tutor theres the internet. And it ain't half bad for free.