I'm not actually interested in immigrating to the U.S. right now. My kids have been telling me to do so. But as far as I understand it is impossible without losing refugee status. In Canadian IRPA laws it says if there is a possibility of gaining a citizenship, but the applicant is not taking any action for it, this will lead to losing status in Canada. Which translates to if you have gained permanent residency in the U.S. then you have choice to stay and become a citizen which (as far as I understand) will make you lose your status in Canada.
TL;DR: No you will lose your status. But don't take my word for it. I'm not a lawyer or something. I'll update if they respond me.