Theoretically yes, but you'd have to work really hard to screw up that badly, and I've never heard of anything like that happening. The recipe for hydro plants is in red science. You need to have produced a bunch of climatology science by then and use water for several other things, so you'll probably have one or more seawater intakes already set up, and all you have to is leave them set up rather than tearing everything down.
In the rare event that you've torn your whole starter base down, I suppose you'd have to refrain from doing a bunch of handcrafting while carrying around essential starting items. It would be a good practice to save your game before completely tearing down your starter base. It may also be a good idea to not tear down your old base until your new one is at least semi-functional, which would mean your new base has seawater intakes set up already.
Another factor that makes this less likely is that you can't hand craft filters, so it's not done spontaneously. It's usually automated pretty early, so you'll have a chest somewhere where you can pick up a stack of filters. So it's common that people will have some spare filters lying around after the very early game. And filters are something you can first produce within the first 45 minutes of the game or so, before you can make hydro plants.
