Based on the standard rules for interrupt effects, I would say yes, and also yes.
Yes, Tatianna can choose to wait until after the OL has spawned monsters to use her ability. She can wait until he says he's going to activate his first monster if she wants (and if he grabs it too fast then the game will rewind to just before he activates that monster so she can vanish.)
If the Overlord goes to activate his first monster without having spawned anything, Tatianna can interrupt just as before, and should she do so, the game will be paused right before the activation, as before. After Tatianna is gone, the OL can choose to continue his old action or do something else, potentially including spawning or activating an entirely different monster.
This is basically the same as the way Tahlia can interrupt a monster's attack and move away - even though the Overlord has already declared he will attack Tahlia and she is no longer within range, the interrupt rewinds to before the attack was declared, so the OL is free to attack someone else or to keep moving the monster.
If you're worried about players getting bogged down in some kind of bluff and counter-bluff mind game of "will she or won't she?" then consider this:
Tatianna teleporting away after spawning is humorous because she's effectively prevented the OL from spawning in a couple of particular places that would otherwise have been available to him. However, the heroes are now one body down and the OL is about to begin moving monsters. Tatianna is in town, where she can do absolutely nothing to help the party until her next turn. Had she stayed in the dungeon, she might have at least absorbed a couple blows. I'm sure there will be times when Tatianna just wants to get out of a room full of monsters (especially if she's the party's runner), but at that point, the question of before or after spawning is probably moot. If she's leaving, she's leaving. If she happens to block some spawn points before she goes, that's just cake.
Also, if the OL declares that he will now activate a monster and Tatianna doesn't use her ability, then he must now activate that monster, thus closing the window to spawn anything. As such, delaying his option to spawn in the hopes that Tatianna will vanish is just tempting fate. There may be one or two constructed scenarios where the spawn points she's blocking are critical for the OL's strategy and then such a gamble might be worth taking, but in general, I think the OL can safely just find somewhere else to spawn and then who cares if she pops out?
I suspect, among a group who are seriously oriented on tactics, it will be fairly obvious when Tatianna wants to use her ability (and when she needs to), so it will also be fairly obvious when the OL can afford to hold off spawning until she's gone. In most circumstances, the best answer will be to not worry about it and just spawn where you can.