The original sentence:
"The senate adopted new rules to prevent representatives from serving on a committee while at the same time maintaining an interest in any company that conducts business that is affected by that committee's decisions."
The sentence as your change is implied:
"The senate adopted new rules to prevent representatives from serving on a committee and at the same time maintaining an interest in any company that conducts business that is affected by that committee's decisions."
I don't see any substantial change in the meaning of that sentence. That's probably because after and, the phrase at the same time takes care of keeping the meaning intact [This was also mentioned by StoneyB in his deleted answer].
However, it's worth to note that using the phrase while at the same time itself is redundant as mentioned here, here and here.