Since Shadow Keeper works fine on BG: EE character files I would guess it would work. I've successfully moved most of my old BG characters over to EE, the hardest thing was re-formatting all my custom portraits, and that's not really a big deal.
No shadowkeeper/whatever needed, import works just fine..with or without abusing the import option to have all you equip/inventory items.
edit: despite of the modified items, which still use the bg2 basic table..you could import a fully equiped 'whatever class' to BG2, with books, items, gems, stones...etc in your pockets. You'd have to abuse the import bug though, as you got stripped of everything, but why should suddenly take all your gear away and waste it, instead of repositioning it in some locker
I guess everyone, myself included, is assuming you have Throne of Bhaal. If you do not, then you can't import a Wild Mage either. So Blackguard is a no-go, and Wild Mage might be if you don't have ToB.
I tried importing a BGEE char into BG2 and it worked fine. Obviously, Blackguards are a no-no. There might be issues with imported items as well but that should be fine since you can just console them if you really want to.
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I would imagine u would have to wait?
Though not sure. Maybe could work? Can't think of any reason why it wouldn't I mean.
Unless it's a blackguard
edit: despite of the modified items, which still use the bg2 basic table..you could import a fully equiped 'whatever class' to BG2, with books, items, gems, stones...etc in your pockets. You'd have to abuse the import bug though, as you got stripped of everything, but why should suddenly take all your gear away and waste it, instead of repositioning it in some locker