Is it possible to marry a foreigner who was denied a visa and cannot apply for three years?

I have a boyfriend who lives in the U.K. He had applied for a visa to visit the United States back in September. Due to a prior arrest (no conviction) for marijuana usage, he had to submit a drug test. They had found extremely small traces of marijuana in his bloodstream and he was denied the visa b/c they said he was a drug user. Now, my boyfriend isn’t a drug user. Six weeks prior to the test, he was out with some friends and he made a mistake. He is a former Gulf War vet who has had medical issues with fibromyalgia as well as other symptoms, while the pot was not for medical use, it helped him.

I am not condoning what he did, nor am I making an excuse for him. The fact he got denied the visa over this did make me upset with him. However, I don’t think that he and I should be punished for three years because of it. We wanted to get married this year. I can only see him a few times a year and the thought of a three year long wait upsets us both. So, my question is, if I go visit him and we get married in the U.K., will that make a difference as far as him gaining entry into the U.S.? Thanks for answering.