As the privites Keys are yours and they are on your computer used to access the remote server, why not? ( you dont send your keys over the network)
So, if you have a full client then you see the whole blockchain and can harvest locally.
If you have a lightweight client then you don't see the whole blockchain and can harvest only by signing data received from remote server(s).
And now imagine that network is sybil-attacked and the attacker can trick you into harvesting on a fork...
I really dont see this as a problem... for any kind of transaction, you'll need the passwork to access the wallet locally ( where is the beloved money). you just need to be sure your node is up to date on blockchain.
Probably, after restart the server, the syncing will be enough to make everything work as expected.
This kind of situation will lead you to harvest nothing, cause you are on a paralel chain, and not on the main blockchain, where transactions happens. Unless everyone will be on a parallel blockchain, which is, im my opnion, almost impossible.