I swear it's just in my head, but when my Windows computer hangs or freezes, I find that opening Task Manager (by either Ctrl-Alt-Del > Task Manager or Ctrl-Shift-Esc) sometimes seems to jog the computer and cause whenever program wasn't responding to start working again, or closes the window I've been furiously clicking X on. Am I making this up, or does simply opening Task Manager actually do something?
I could see that happening if you were getting slow downs due to disk problems (as opening it may change how the disk is being accessed, making it skip or release a block it's fighting to use). It could also cause something eating all CPU to release some of it long enough to release a lock state. But neither of these scenarios would necessarily be Task Manager-specific.
One thing 'special' about Task Manager is that it's always launched with a "High" priority flag, giving it higher priority for CPU usage than other software (usually running with "Normal" priority). This increases the chance that it may rob enough resources that it may cause the locked program to unlock (by interrupting a file-system race condition, or thread spinlock for example).
A lot of it IS probably in your head as well. Sometimes Task Manager won't open until the pause has passed, making it SEEM like the Task Manager caused things to advance, when in reality it was just waiting in turn. Also, often things that are "not responding" for a long time actually finish what they were doing in the time it takes between you giving up waiting, and trying to kill the process with Task Manager. :)