Training with a mind set that even if you get cut you will continue on is a good idea.
Training with the idea of letting the other guy cut you so you can get a cut in is a stupid idea.
Training in such a manner that you do not expect the other guy to collapse after you stab or slash him is a great idea. How many scenarios seem to stop as soon as the first cut is made? People don't just collapse after being cut, so why stop at the first cut when you train?
People tend not to feel a lot of pain until after the fight. As Don Rearic pointed out, most folks do not know they have been stabbed until they see their own blood- then they faint. It is a dead issue to deal too much on the subject.
Since this thread touched on ASP batons, I will point out some tips.
If you do not want to destroy your bag, or can't afford a traiingn bag, an old tire lashed to a tree works well.
Don't use cheap copies. Even hitting something lightly with one causes them to bend. Go with quality like the ASP brand and not cheapies made in Taiwan.
ASP batons can and do bend under extreme circumstances. Street fights can generally be considered extreme circumstances.
I have an associate who is in law enfocement who keeps a bent ASP baton on his desk. The guy he used in on was under the influence and trashed an entire store before he went down. I think he was int he hospital for months afterwards, but that did not help my friend who was staring at the bent peice of metal in his hands.