I would leave him home too. You might find it difficult to relax and share if he's there peering over your shoulder. There's also the chance that he may use any info there against you at a later stage...not sure if he's that kind of bloke though.
My exA used to tell me I was nuts for coming on this site, that al-anon was about him and how dare I want to go to a support group to sit around and try and figure him out...
He'd also be nice sometimes and listen whilst I explained things about codependency only to use them against me or throw them in my face the next time he was in a rage.
I soon learnt that his stuff is his and mine was mine and it was better kept that way.
If your BF is being sincere then that is a nice offer but I would still politely decline and point him towards an AA meeting if he's that interesting in support groups.