NO it will not set off the limp mode,,as long as you are going somewhat straight, I mean don't try to drift. I in all my tire testing I tested 205/50-16 24.1" tall , BE CAREFUL ALL YOU DO IS SPIN.
the best and only tire size you should use is a 255/50-16 drag radials if you are using 16" rims,, any thing smaller will spin also. there are 17 18 and 19 drag radles,, also i would not go smaller than a 25.7 tall and not taller than 26.2
jim