I'd suspect not for very long. The dissolved oxygen level in the club soda would be pretty low, I'd expect, and the club soda would also likely be somewhat more acidic than the fish would be used to. I suppose if one used a species of fish that was adapted to a somewhat acidic environment (not sure how acidic it would be, offhand) and that had low oxygen requirements, it might survive for a reasonable while.

If you weren't expecting a serious answer, well, all I have to say is that questions in my house (by which I mean one of my areas of expertise slightly less ignorance) tend to inspire me to put on my Serious Hat.