The BFS (spaceship, i.e. second stage) is supposedly going to have enough performance to make orbit on its own as an SSTO, with a tiny payload. It probably won’t ever be used that way, though.
You need supplies to keep those humans alive for a week, and a huge amount of fuel to boost the ship into a moon-intersecting orbit. Not a tiny payload by any means.
To get other BFSes up there with enough fuel to transfer a useful amount would require them to use the first stage booster instead of just being SSTO.
Really there's no point to doing an SSTO launch in practice since the BFR first stage will in theory be just as reusable (if not more so) than the BFS second stage. Using the first stage booster greatly improves payload to orbit and has relatively low marginal cost once you've built and tested the whole system.
For a single launch, sure.
What happens if there are regular launches?
Logistically, to me it seems that it would be a great idea to have a refueling station in orbit which is supplied by BFR cargo ships ..say.. once a month.
Launching a BFR for each launch of BFS would require a lot of transportation and duplicated effort.
Is this intuition wrong?