Look at Shield, etcetera; there's lots of cases where things are retroactive. But the one you gave isn't one of them.
But you're also assuming that "provided" and "completed" are the same thing, and I don't think that's actually justified at all. If pointing at targets is part of the S component, then if you get paralyzed between two beams, the later beams won't be aimable because you can't move to point. So there's the components necessary for the initial "casting", but there may be additional things happening during the "release of energy".
So I think the real answer is, if you're interrupted during the part of the spell where the effects are manifesting, the spell's already fired and does take effect, but it may stop taking effect before you're done aiming at targets or whatever.
So again, the problem is the assumption that any failure to complete the part of the spell where you're using verbal or somatic components to, say, aim at additional targets, causes the components not to be "provided". Provided just means they're there during casting.
But you're also assuming that "provided" and "completed" are the same thing, and I don't think that's actually justified at all. If pointing at targets is part of the S component, then if you get paralyzed between two beams, the later beams won't be aimable because you can't move to point. So there's the components necessary for the initial "casting", but there may be additional things happening during the "release of energy".
So I think the real answer is, if you're interrupted during the part of the spell where the effects are manifesting, the spell's already fired and does take effect, but it may stop taking effect before you're done aiming at targets or whatever.
So again, the problem is the assumption that any failure to complete the part of the spell where you're using verbal or somatic components to, say, aim at additional targets, causes the components not to be "provided". Provided just means they're there during casting.