I personally have done both. As mentioned by Glen, I like to strop while the lather is on my face softening up my beard.
I also, to save time, have stropped my razor earlier in day, as you said, on my way back from the bathroom. I think either way is fine. I've bought razors from respected restorers who've stropped them for me before shipping, and I still strop it before use because of crap on the blade. I had one such razor one day, and it looked as if the blade was chipped, When I looked at it through my loupe, I could see it was just some kind of debris, probably would have rinsed off, So, I guess it's not a bad idea to maybe just hit the strop 10x right before the blade hits your face even if you "Pre Stropped"
Enjoy....Rich