I would take that bet. The observable universe is estimated to have 10^21 stars and the actual universe is infinite.
But of course you are right about the absolutely staggering number of stars in the observable universe.
I don't see how causality plays into the question at hand. The parent post didn't bet that we could interact with alien life, but if it exists at all. If it can be demonstrated that the actual universe is infinite, it will follow that alien live exist, independent of if we can interact with it.
I highly doubt the actual universe is really infinite, however. Incomprehensibly big, yes.