If washing machine is other side of kitchen, can I just connect it when I want to use it or does it always have to be plumbed in?

As long as the shut off valve(s) hold and there is a legitimate PTRAP on the waste line and you don't go months between use, I don't see any reason to be concerned with periodically connecting/disconnecting the washing machine. If you plan on moving the machine in between uses then you may end up damaging the floor if not careful, but otherwise, you should be all set.

Mark

As Mark noted, I'd be worried more about proper drainage than supply.

Drainage is not likely an issue. A washing machine can pump out water to a height of nearly 10'. The supplied drain hose does not require a trap but will be too short to reach over the kitchen sink front edge because of the built in180 degree bend on its end, an extension may be needed and of course the sink is already trapped.