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. :)
@Sonic42 I am experiencing exactly the same behavior on every windows machine I ever owned... Even when some program hangs for minutes, opening the task manager would trigger the continuation of the process... Very strange. It's just in our head I think... ^_^ I am not statistfied with the accepted answer :-/ This can't be the reason, since my windows is running on an SSD. – WoIIe – 2019-07-05T15:06:50.977
7It could actually be the opposite: Task Manager cannot open until the system starts responding normally. – user1686 – 2012-01-22T19:37:18.143