It would make a difference to the handling at higher speeds.
My mate was in the process of swapping his over (old bt's to new) & did them a bit at a time & the truck would get at frantic wobble at 40ish that was apparently quite alarming & hard to control... All new tyres going on were balanced, as were all old ones coming off, but the problem only occured when the tyre swapping started
It looked quite odd as well following him with the back end skipping about all over... once all the tyres were done the problem stopped :dunno:
All at once I'd have thought... or at least the back 8 at once (but then its only 2 more & you're done (minus spares o'course).