Sometimes yes, sometimes no. It depends. If it's just saying the same word in just changing the emphasis (like aluminum), then usually not. The big however to that one is that to me the way people born and bred in Yorkshire say their o's sounds, to my ear, a lot like the way my aunt, grandfather and great aunts and uncles from Minnesota would say theirs. Since I thought it was an interesting sound growing up, I mimicked it. And then, after working in a school here in the UK for nearly a school year I found myself saying 'I don't know' the way the kids did when I was asking them why they did what they did. It particularly happens I noticed if I'm feeling exasperated. I think it's bizzare the way my brain has twisted that one around. My dh just howled with laughter the first time I came out with that one.
If it's a different word altogether then yes, definitely I've picked up more than my fair share. I've been known to call friends muppets or to say cheers or ta instead of thank you, especially if I am not thinking (like when I say thank you to a bus driver). One I wished I didn't say was b***ger. To me, it and the term loo just sound strange in an American accent.