The thing is, an SF MP can't vote or debate because they, by policy, refuse to attend.
You're correct that the party has representatives in the other bodies which it does recognise but those aren't the same people.
So for example Órfhlaith Begley was elected MP for West Tyrone. Her voters will have known she's not going to Westminster, and she didn't - but she's not in some parallel institution instead, AFAIK there isn't one. Nicola Brogan represents West Tyrone as an MLA in Stormont, because Sinn Féin does recognise the Assembly and you can't say well but there's a body in Dublin. Dublin doesn't control West Tyrone so what would she even do there?
So for example Órfhlaith Begley was elected MP for West Tyrone. Her voters will have known she's not going to Westminster, and she didn't - but she's not in some parallel institution instead, AFAIK there isn't one. Nicola Brogan represents West Tyrone as an MLA in Stormont, because Sinn Féin does recognise the Assembly and you can't say well but there's a body in Dublin. Dublin doesn't control West Tyrone so what would she even do there?