Q:

Can Battlestars actually fly in the atmosphere

In Blood And Chrome during the beginning, we see an (original style) Basestar hovering above Caprica City, and during The Plan, We see a (modern) Basestar flying through the sky at breakneck speed. 
So could a Colonial Battlestar hover or fly in the atmosphere?

A:

In the Season 3 episode Exodus, we see the Galactica do an FTL jump into the atmosphere of New Caprica.
As it begins to launch its Vipers, it immediately begins to drop like a rock, and only remains in atmosphere long enough to make another FTL jump to exit the atmosphere.
The fact that it fails to maintain altitude in the mean time strongly implies that Battlestars are incapable of atmospheric flight.

