If you were to create a website based solely on your forum and applied to google adsense would they accept you? Also, if you are interested in the subject of your forum, is it a good idea to make a website dedicated mainly to a forum? Could you make any where near the same money of a website that isn't forum-based?
active forums are great for traffic google loves to eat up all that fresh content. but starting a forum from scratch is gonna be one of the hardest things you will ever try to do. its better to start a website get the page listed in google for your search terms and then add a forum. but either way adsense will accept you just so long as you read there terms of service like no adds on search pages or sign up pages. read thurally.
Forums IMO are one of the hardest sites to attract users. They start with one member... you. Why would anybody join? That is the main hurdle to get over. With only a forum, getting indexed in SEs will be rather difficult as well. Unless you can create a lot of indepth, informative posts all the time. Id suggest finding a unique, targetable niche and have your index page filled with articles and useful information. Then having a link into your forum.
starting a forum is tough, not only cuz theres so many, but also because if it gets a decent size a shared server wont cut it.