The radiation remained, which is why Kirk couldn't run in there and haul him out.
Actually, it wasn't there. Before Spock puts the engines back on line Scotty is passing out from radiation. The whole of engineering is covered in it. After Spock put the mains online the radiation is only confined to the chamber room. So where did it go and why did scotty have to disconnect the perfectly fine engines if the radiation was only a problem in that one, sealed off area?
I don't see any one of them sending some trainee kid in there to die. They'd already lost one that day. Also, who can we expect to be the best-qualified to make repairs quickly enough to make the difference, other than Scott or Spock? And Scott was incapacitated when Spock arrived. That made the decision pretty simple for Spock.
Yeah, Scotty is out cold, and just happens the wake up as someone else starts doing his job, wink wink.
The point here is, someone in engineering should have done the job. 1 grunt or 20. That's still less than 400 other people. Kirk just sitting there and waiting for death, hoping his crew would step up was irresponsible. Seems to me loosing a few more cadets is worth loosing a whole ship full of them.