Can changing the tire size from stock P215/65R16 to LT245/75R16 cause this code?

I know going to the larger tire size changed my speedometer,acceleration, stopping distance, ect. ect. What's the largest tire size that can be installed, before these changes occur?

it's ALWAYS a good idea to start with the details of the vehicle being discussed.

As a "generic" code a P0720 is related to the transmission output shaft speed sensor and I would say, yes, in theory at least, it's possible that going from a 27" (215/65R16) tire to 31 (245/75R16) could cause it.  I'll withhold any further comment until I know what vehicle I'm dealing with.