No, cutting the chain IS accelerating the process. Usually, if a soul doesn't get one of those "Soul Burial" things then the chain just begins to erode. Once it erodes completely you become a hollow. Cutting it speads up the process to a few days rather than months.

Well, that may be true, but he still has SOME ties to his body, but I do see what you mean by him having to choose between Soul Reaper and Hollow. It would definately mean that he's dead now. But, the thing is, Ichigo still needs help getting out of his body. I don't really want to spoil much for you, but Soul Reapers seem to be able to just jump out of their gigais, while Ichigo still needs something to force him out. Though, it may just be because he's using a real body and not a fake one, I think it's because his soul is still hanging onto some sort of connection.