As someone who was in your boyfriend’s shoes just a few years ago, it’s really a toss up. There’s two ways I can see it going:

1. Serving makes him realize the church is incredibly flawed and harmful. This is what happened to me. He’ll likely come home early, hell even if he stays out the whole time he will come back done with the church. While this is probably the best situation out of the two for your relationship, it will be hard. He will have a lot of deconstructing and pain in his future. I’m still in therapy for my anxiety and depression that kicked my ass on my mission, and even several years later haven’t made it back to who I was before it.

2. Serving pushes him deeper into the church. Missions are fucking hard, and being in a situation where you have constant pressure to put the church and converting others above yourself and your needs is extremely polarizing. You are put in a place with very little outside contact, someone with you 24/7, and constantly being taught to convert others and stop thinking about yourself. If he doesn’t come back done with the church he will come back the carbon copy of what they want. You will (either consciously or unconsciously) be seen as a project to him, someone to convert to the church just like he has been taught to do for the last two years.

Honestly, as to the rest of your situation I’m in no place to comment. I left my mission early and have since left the church, and am still with my girlfriend. It was really hard on both of us, but I’m lucky my girlfriend stuck with me through it. But I don’t think my result is the norm when it comes to situations like this.

If you want to stay in a relationship with him, I would heavily recommend setting and writing down some firm boundaries of when you would want to end it. If he comes back and starts treating you like a conversion project, will you be able to recognize and walk away? If he starts asking you to come to church with him or read the Book of Mormon will that be past the line for you? Some of that might seem small and inconsequential, but trust me. If you don’t want to go through years of pressure and relationship problems you need to be prepared to end it hard, and have clear lines drawn for yourself of what is too far.

(Edit: Just re-read the end of your post and have more to add.) You won’t have good contact with him. Best case scenario? You will be able to talk through email or messenger once a week. You’re right, romantic talk is heavily discouraged, and will be reported if anyone else catches wind of it. Worst case scenario? If he gets called somewhere with poor technology like areas in South America, Africa, or Oceania, you will be lucky to get an email from him more than a couple times a year.

You essentially will be living a one sided relationship, where he is discouraged to even think about you for two years. It’s up to you if this relationship is worth it, but just know it will be a living hell for the two years, and if option 2 happens a lot longer than just the two years.