No, that will not work the way you think it will. You will still have the same issue but in different locations. This is called a wave interference pattern. Waves from two sources will add together in some places and negate each other in other places. I don't think it's that big of a deal though. If it sounds weird in one place then move a few feet over and it will be different. Just make sure you have your mic in a place where it sounds good. I see lots of bands do this on stage so it can be made to it work if you really want to.
Personally, I would keep my stuff on one side and rely on the side fills as needed. If they can't handle it then have the sound guys get better ones and have your monitor guy dial 'em in better. Also, you might want to look into an in-ear monitor system. No side-fills needed with those and you will have a consistent sound everywhere.
Personally, I would keep my stuff on one side and rely on the side fills as needed. If they can't handle it then have the sound guys get better ones and have your monitor guy dial 'em in better. Also, you might want to look into an in-ear monitor system. No side-fills needed with those and you will have a consistent sound everywhere.