We (Americans) do fine with most British words (lorry, boot).
A few still take me by surprise until I remember (jumper, vest, pants), but then, I read a lot of British novels.
Some people will be utterly confused or not know why you think it's funny when they referred to someone's "pants."
However, it's nothing to worry about, and you'll have the opportunity to fix any misunderstanding. If you're modeling your pronunication on British English, I'd stick with BrE vocabulary as well. (It's the same for the vast majority of the words. Even with your example of "faucet" and "tap," both are widely used in the US.)