Hi there π
Yes I did the K1 Visa after getting engaged to someone serving hard time (life sentence without the possibility of parole at the time). As long as it is not anything domestic violence related, you should be okay to go, and as long as you don't have a criminal record yourself of course. You'll also have to find someone to co-sponsor you, as I'm guessing he doesn't have income or very little.
I encountered some difficulties, however, when I applied for the green card and my husband couldn't attend the interview to the USCIS office with me. My green card was denied because of that, so I had to hire an attorney to appeal their decision and we won! Some people would say it's safer to go for a spouse visa in our situation, because at least there's no joint interview required before the green card's obtention. Today I have my 10-year GC and don't regret a thing, it's totally doable in the end but be prepared to have to go through many hoops because they surely won't make it any easy on you.
Also, gather as much evidence as you can. All of your letters, emails, phone bills, pictures of you two together, gifts you sent him, gifts he sent you, etc.