He may sincerely plan to stop drinking if you go ahead and marry him—but how do you know he will? The answer is—you don't, not until it's too late.
And the reality is that someone who has a problem with alcohol right now, will probably still have it in the future. Alcohol can be very addictive, and even if he wanted to stop he might not be able to do so without outside help. After all, if he says he'll stop drinking after you are married, why doesn't he prove his love for you by stopping right now? The Bible warns, "Wine is a mocker and beer a brawler; whoever is led astray by them is not wise" (Proverbs 20:1).
Almost every week I get at least one letter from someone whose spouse promised to quit some harmful habit once they were married—but didn't. Sometimes it's alcohol or drugs or some other destructive habit; sometimes it's a character flaw like anger or jealousy or greed. Whatever the cause, now the husband or wife finds themselves trapped. Why take that risk?
Instead, I urge you to commit your life to Jesus Christ and seek His will for your life—including your marriage. Urge your boyfriend to give his life to Jesus also, for he needs God's help to get his life in order. Even if it isn't God's will for you to be married to each other, God still loves you both, and wants you both to come to know Him and follow Him every day.