Sure, they could do it if they want. It's fictional afterall, so they can do whatever they want.
I just think they threw Alexa in there as good filler to give Bayley a high profile opponent (and possibly a high profile win), because Alexa seems to have some sort of angle going with Nikki on RAW, so I don't think they're having her switch brands.
But ya never know. Maybe it's sort of a swap for Smackdown losing Becky. Seeing Charlotte and Alexa on the same brand could be interesting.