Desperate Need of Relationship Advice!... please read?

My boyfriend and I have been together for about 3 years. He and I were best friends 2 years before we got in a relationship. To us, it seemed like being together was a great idea because we already knew each other so well. Up until about 7 months ago, things are starting to change for the worst. We both have full-time jobs and work 2 entirely different shifts, I work mornings he work nights. When I'm coming home, he's leaving out for work. And when he comes in, I'm in bed asleep. We barely spend time together and we are hardly having sex at ALL. I found out that he's been being extra flirty with the ladies that he works with. I even saw messages in his phone and on a social website with a girl in particular. I confronted him about it. He came clean and said that he was attracted to her, but it just was innocent flirting. He says that the lack of sex in our relationship makes him feel like I don't want him sexually, and it makes him feel good when the women at his job finds him sexually attractive. We both made suggestions on how to make things work out better so that this will no longer be an issue. In the midst of our discussion, he actually said that he wants to marry me.... like, as soon as possible. When I asked him why he wanted to marry me, he said because he loves me and he can't imagine living life without me (ect. ect.)Here's what I wanted to ask:If I had sex with him as often as he'd like, would that make him less likely to cheat or be extra flirty? Or is this just a way for him to get what he wants sexually?Should I marry him? I want to, but I wouldn't want him to get himself in a situation that he'd regret later. We've talked about it before this situation came up, but I don't want him to be marrying me in vain.I really need advice. Please help.*And for all the Zodiac fans out there, I'm a Pisces and he's a Sagittarius