I don't know that much about the architecture of the Lemmy or Kbin software, but I would imagine it does some kind of sync operation that's not time sensitive. So I would expect you could bring a server up and down at some cycle and still do all the pushes and pulls as required.

Though in practice I think I'd just set up a server that's always on. I mean you could probably do it easily enough with an R-Pi and DynDNS. I don't believe the software is all that demanding until there's a big user load.