Offhand, that's pretty much the plan for a black start.
Something about bringing up a designated plant and feeding the output over 'cranking' lines that other plants along the route can synchronize their output against. Then gradually adding load and source until the system is meta-stable again.
Edit: additional data
Not only synchronize, but also use for internal needs like all the pumps and particularly the 'excitation current' that establishes the magnetic field for the generator. It allows control over the output voltage. There are also other drawbacks to the more obvious solution of fixed magnets which can be oversimplified as 'ware'.
The problem is not so much the concept, as how tricky it would be to add the loads back in at just the right rate to not trip some or all the generation back off again. Sure once you have enough generation and load already online, adding the rest is relatively straightforward. Still need to be careful, but after a certain point it would look to utility operators much like the usual work restoring loads and sources after a large area blackout.
The trickiness seems worst close to the very beginning when even relatively small misestimation of a chunk of load being restored would have a proportionally bigger impact. Many loads are not completely predictable, so presumably they would need to favor bringing some of the more stable loads online early so that normal variation from the loads that can only be predicted well in aggregate won't vary enough to trip everything back offline.
The trickiness seems worst close to the very beginning when even relatively small misestimation of a chunk of load being restored would have a proportionally bigger impact. Many loads are not completely predictable, so presumably they would need to favor bringing some of the more stable loads online early so that normal variation from the loads that can only be predicted well in aggregate won't vary enough to trip everything back offline.