In my opinion, this is a really loaded question.
As converters are basically the final step into the computer, they can obviously make a big difference--specifically between something professional and consumer/prosumer. However, there are so many steps before conversion that need to be considered every bit as much as conversion (if not WAY more than conversion).
How does the source ACTUALLY sound in the room? Is the room controlled? Is the performance good? Is the mic placed and responding how you want it to sound? How is the preamp affecting the signal--is it complimenting, or is it ruining what you're trying to capture because it's a crappy, noisy design?
So in summary, yes, a good adc converter can definitely improve the capturing of a source; however, there are many other factors that must be considered and examined before any one of us (from afar) can say, "Yes, upgrading to a better converter will accomplish ______."
To me, it sounds like you need to concentrate more on dialing in your sounds and mixing in post. I've heard a lot of great records recorded on what would typically be considered sub-par converters... just depends on the people using them and/or making the mixes.
Then again, I do understand the concern when layering sound after sound on top of each other... clarity does come into play for sure in this case. Best bet is to do a comparison yourself and see if you hear a difference. *But I have to stress again other factors: like how is your mixing room treated? What speakers are you using? Etc.