Q: If I play 2 & Use ‘Em and one of the cards causes me to win, but the other negates it, can I win?

A: You can absolutely win. You just have to play the card that makes you win as the FIRST card. At that point, you just win, and you’re not required to play the other card you drew for Draw 2 & Use Em, since the game is now over.

The situation would be similar if your conundrum was in the middle of Draw 3 Play 2, though this issue is less likely to confuse people, since it’s pretty clear that they have (slightly) more options. Fizzbin also creates a similar situation.