figuring out which levels you beat as white racoon mario

It's my understanding that if you beat New Super Mario World 2 having gotten any gold coins as a white racoon mario that the mushroom houses get destroyed after you use them. If you get all the gold coins without using white racoon mario you can use each one as many times as you see fit.

My question is... is it possible to go back and get the gold coins (or the silver coins that are in their stead after you've gotten them once) and unlock this "mode" even after you've beaten the game, having already gotten a few gold coins as white racoon mario?

I believe what you are trying to ask is, do you have to collect the gold coins as normal Mario to have unlimited toad houses? The answer is, no you do not. To get unlimited toad houses, you have to complete the game by collecting all gold coins (collecting them as white raccoon Mario doesn't make a difference, but some coins need other Mario abilities such as using the fire flower), and completing all levels without using the white raccoon suit. So it doesn't matter if you collect the gold coins as white raccoon Mario. It only matters that you do collect them, and that you can finish each level as normal Mario.

TIP: To check if you completed a level as "Normal Mario", you can see if the circle that you are on is red or blue. Blue means you have completed it normally, and red means that you haven't.