No, not really. Not if they are a real practicing Mormon. The church would tell their husband or wife they had to become a Mormon or possibly kick them out of the church. It depends which branch of Mormon too. Some are very strict and others much more lax.
Of course they can. I'm LDS and I'm marrying a non-Mormon in a few months. She understands how important the church is to me, and I understand she's not interested in any religion. - As far as the church is concerned people are encouraged to marry in the temple, which requires both to be practicing Mormons, there is no rule requiring they do. I was married in the temple to my late wife, and I won't be to my next wife. - It's not an issue that the church has any prohibition about. The other person who answered this question before me answered with a totally false answer. There is no rule about marrying a non-Mormon.