My comment about 'no effect on the amp' meant that this situation is not the same as running two passive speakers in parallel off a single channel, which certainly could cause adverse effects as you well know.
In my experience any audible difference in performance in either the mains or the subwoofer from simply plugging another cable from the amp into a powered subwoofer has been completely negligible. And at studio SPL I have never had a problem running good quality power amps full range, without using external crossovers. Besides, in my case I almost always am running my high end monitors full range, I don't want them pre-filtered as a sub/sat installation. Maybe you have different experiences.
But if the OP does want to run sub/sat then AFAIK almost every powered subwoofer made has speaker level connections and internal crossovers already included just for these kinds of configurations. Not as fully capable or highest quality perhaps as a dedicated bass management system, but typically completely usable for most practical studio installations IMO.
Oh, and this option:
Originally Posted by bluechips
Can I split the signal coming from the mixing console to the inputs of the amp and then sending the split signal to the sub?
Yes. Can just use passive Y-splitters. Still need to balance the volume and frequency of the sub of course. And if you turn the sub's power off then the volume level might change in the mains.