I don't know about that.
His very name, "Dajbog" essentially means 'The Giving God', or something along those lines.
It would make sense, then, that this god was somehow associated with perhaps, giving gifts of luck, or maybe even some kind of wealth.
So sayings such as "nek' bog da" or "dajbog" "dajbože" "da bog da" could very well be directly referring to this old Slavic Deity, whose very name is associated with giving.

In contrast to that, the God of The Bible doesn't give all that much, does he?

The phrase "may god" exists in many languages where the speakers are largely followers of one of the Abrahamic religions. Also, the phrase claims there is one god which goes against Slavic polytheism idea of multiple gods. I just don't see how they are related.