In this hypothetical scenario, I think a team would be "allowed" to play with 10 men if the 11th man was on the pitch at the start of the game, if only for a second. I assume a player leaving the field of play is allowed to return at any time during the course of the game....or is there a time limit...?
But, as you say, it's not about starting with 10 men per se, it's about teams adopting the same tactics with 11 men as they often do when reduced to 10 men.
Meanwhile, back in the real world... :-)