I believe this would be allowed, but just wanted to confirm it here.

Let's say I place Ambush on a figure with Stealth and has a Wild Card team ability. Could I use Ambush to make an attack, then Wild Card the Batman Ally team ability to effectively get Stealth back during the opponent's turn?

Sure, you could declare Bat-Ally TA, it's not 'real' stealth, so wouldn't be countered.

You could use the Batman TA to block LOF to your character, yes. However, please note that the Batman TA does not actually grant the power Stealth; it has an effect that is similar to that power and that's it.

Right, that's why i used "effectively" in my OP. Just like how Batman TA has no bearing on the Infiltration BFC.