If your system is setup correctly you should at least check logs and do every thing you can to try and detect an intrusion whenever there is a possible vulnerability. This is part of a sysadmins job.
For instance, after the whole Debian SSL fiasco we checked over all of our logs for any odd or unknown usage and had everyone change their passwords and replaced all keys.
Of course the severity of the vulnerability dictates the actions that are taken.
Basically a good sysadmin will have detection measures in place and a plan to deal with intrusions because no system is completely secure. And a sysadmins job is to monitor all security issues that occur on software used by the systems that he is in control of. This must be in place so that we can remain reasonably safe and secure as can be expected.
So, absolutely yes, every time there is a critical security issue that could have affected your systems you should be spending some extra time to make sure the systems have not been compromised and cleaning up what you can. I wouldn't want a sysadmin working for me that didn't do his job completely as I have explained.
If I have not seen as far as others, it is because giants were standing on my shoulders. -- Hal Abelson