I have been playing Elite Dangerous on the Xbox for awhile, but I'm thinking about moving to PC. If I get the game for PC, will I be able to use the same account - and, more importantly, carry over game progress, ships, etc.?
No. There is no account sync between Xbox and PC. Mac and PC are the same account, though.
You can contact support and have them liquidate one account and move all the credits into the other. That would put your Xbox account back in the starter sidewinder with nothing, and would only move money into your PC account. A friend that moved from Xbox to PC had that done.
That liquidation definitely will not carry over any ranks, faction relationships, etc etc...
I think when they liquidate the Xbox account, it fully resets, losing everything, not just assets.