University knowledge of student and/or staff viewing free online journal article databases

There easily could be, so don't do marginally legal things on your university's network. Mine doesn't appear to do more than shut down bot nets and torrent hosting, but it's not hard to track the rest. It's mostly only in the university's interest to stop crimes and copyright infringement committed on its network so that it doesn't have to deal with law enforcement and/or lawsuits (i.e. paperwork and cooperation). I don't think Sci-Hub and LibGen have risen to that level quite yet. You might get away with it for awhile, but if enough people start accessing scientific content that way, then the paperwork will start to flow in, and the accesses will start getting shut down.

Enhancing on @BillBarth's answer: while universities do not typically monitor access to services on their websites, they are quite capable of doing so when the need or desire arises.

The handling of Aaron Swartz's JSTOR mass-downloading by MIT may be instructive here: MIT information services was apparently fairly unexcited about the incident for quite a while, treating it as relatively routine network misbehavior. Eventually, however, it changed positions and began carefully monitoring him and cooperating with the prosecution that would eventually lead to arrest, massive charges, and Aaron Swartz's suicide.