The Live Lounge is usually acoustic, although sometimes it is full band electric sets recorded at Maida Vale*. I would expect Bon Jovi's performance to be electric.
Fearne Cotton has started a thing where every friday morning at 11am ('Bon Jovi-o'clock!') she plays 'Living On A Prayer'. They confirmed on the show this morning at the band would be doing the Live Lounge and would definatly be playing Livin' On A Prayer. After all the airplay Cotton gives it i cannot see it just being a stripped down acoustic version.
She also played WWBTF this week on her show.

'New' Bon Jovi, let alone a live performance too, on BBC Radio 1 is a BIG DEAL!


*The times last month when it was done from someone's dig's (eg the Kasabian edition Ferret mentioned) was part of a special 'Live Lounge Tour', where they did it from a different persons house each week for Jo Whiley's last week of shows in that slot.