IMHO it depends
1) does the vehicle have ABS or any speed sensors that would trigger a fault if the tire diameters aren't close enough
2) Does the vehicle have positraction or auto locker rear diff? again difference could cause premature where on the clutch plates
3) Again as mentioned, might be an issue on a dually.
If none of the above apply I can't think offhand of an issue on a short term basis.
And in an emergency, again even with any of the above you'd probably be ok to get to a repair point.
Remember, even if you started with exactly the same tires all around, once the ones in use are worn to near wear limit, the overall diameter of the tires will be smaller than the un used spare anyway.
As an example suppose a tire has 8/32 of useable tread depth (in the range of a new tire) when that it worn away overall diameter is down by 16/32 = 1/2 inch.
2011 Keystone Outback 295RE
2004 14' bikehauler with full living quarters
2015.5 Denali 4x4 CC/SB Duramax/Allison
2004.5 Silverado 4x4 CC/SB Duramax/Allison passed on to our Son!