The rules state that if there are no cylon ships on the main gameboard, any crisis cards that activate cylon ships move the pursuit track up by one.

If there are cylon ships on the main gameboard, then the only way to move the pursuit track is by utilizing the basestar bridge.

My question is, while there are cylon ships on the main gameboard, can a revealed cylon use the Cylon Fleet board to continue increasing the pursuit track?

I'm not completely sure I understand the question, but here's what the faq has to say on the subject:

Q: How does the Cylon Fleet location affect the Cylon Fleet
game board?
A; When a Cylon player uses the Cylon Fleet location on the
main game board to activate all Cylon ships of a certain type,
it is the same as resolving the activation icon of that type.
For example, activating raiders is the same as resolving the
activate raiders icon. In this way, using the ability on the Cylon
Fleet location to activate all ships may result in ships of that
type being placed on the Cylon Fleet game board and advanc-
ing the Pursuit track. When the Cylon Fleet location is used
to launch 2 raiders and 1 heavy raider from each basestar, it
only applies to basestars on the main game board and in no
case are ships added to the Cylon Fleet game board or is the
Pursuit track advanced as a result.

You're right, I didn't explain myself correctly. I'm not talking about "Cylon Fleet" location on the main game board. I'm asking about the "Basestar Bridge" location on the cylon fleet gameboard.

Basically, the way we play, the only time the cylon fleet pursuit track advances is if there are absolutly NO cylon pieces on the main game board.

What I'm trying to find out is if the cylon player can use the Basestar Bridge location, roll a 6, and increase the cylon jump track while there are still cylon ships on the main game board

Oh, yes, totally.

Well, first, it's important to note that main board doesn't have to be completely empty for cylon ship activations to advance pursuit; for example, if there are raiders on the main game board, the pursuit track will still advance if you draw a basestar or heavy raider activation icon.

But that restriction only applies to that particular method of advancing the track; the basestar bridge can move the track even if all three kinds of ships are on the main board.

subochre is 100% correct,

Having cylon ships on the main board *slows* the pursuit track considerably as activations of that particular ship type will not advance the track but all others (eg base star if there are no base stars on the main board) will still advance it as will manual methods (base star bridge, crisis cards that tell you to "advance the pursuit track", i think there are only 1-2 crisis that do this tho).

note when you have any base stars on the main board raider/heavy raider icons will launch the appropriate ship type from the base star if none exist rather than advance the track