I've just ordered the Olympus 14-150 but it won't be here for a week. I already have a decent 52mm polarizer and was wondering what problems I would run into if I got a 58mm-52mm step down ring to use it.

Am I correct in thinking the worst thing that will happen is vignetting at the widest end of the zoom? Will it be much?

It's defenetly going to vignette. Try it and decide how much you're willing to tolerate.