If they measure to the same diameter, you should be fine, as this means the tires will be rotating at the same speed (or close enough). The risk is in having a wheel or wheels turning at different speeds. All four must be the same overall diameter. The system is likely designed to handle some variance, as the wheels rotate at different speeds every time you go around a corner (side-to-side), but there's a limit in there somewhere.
Think about why you want a flatbed when the car breaks down. If the fronts are locked in place and the rears are spinning, the result is your least favorite set of paperweights and doorstops. It's the same principle. If you ran different sized tires, I suspect you might get away with it for a little bit, maybe an emergency trip to the parts store or work, but it's not an ideal long term solution.
I've got an annoying high speed shimmy coming from the front right that I thought might have been wheel balance, so I swapped in a different pair of fronts. I got halfway across Phoenix with something like 215/55/15s on the front and 205/55/15s on the rear before I realized there's a 10mm difference in tread width on those, meaning my front tires were 5.5mm taller than the rears. I did about 60 miles at 70mph in 100°F with the AC on before I got back home to swap back over to the matching pair. The car still has the shimmy (probably bent lugs or a worn bushing or some other stupid BS), but even if the tires fixed the problem, there was no way I wanted to keep driving like that.
Anyway, not as technical as toybreaker, but I hope it helps.
