re: For the gurus: Can a transfer qb bring plays with him?

I'm sure he does/did.

I also have no doubt that the similarity between the actual plays run were of no shock.

One thing that will, always, be different is timing. How fast does back get to mesh point, etc.

And one thing many discount, that can be very helpful is the playcalls, namely how they are communicated. Some teams run players in and out (very few in P5 anymore), most signal from sideline, with or without dummy calls. Some signal formation and play separately with a game-coordinator (e.g. "passing game coordinator") getting people ready. Every team has their system of who signals what and especially who gets the substitutions ready to enter.

tOSU uses placards for the most part; probably just either play or formation with signals from OC for the other. The reason you see 2 (or more) placards may be dummy calls, or it requires 2 (or more) calls for a personnel grouping (e.g., one is for OL, one is for backs/WRs).

What Burrow, or any transfer, could possibly bring to the table is a more efficient way of communicating formations and plays.