A friend replaced her Comcast TV box with an over-the-air antenna but
continues to use Comcast Internet service. This leaves her
Comcast-supplied splitter with an unterminated socket - does it matter?
Should I bother to terminate it?

(A barrel connector isn't a good replacement for the splitter as the
splitter provides a grounding point.)

It is a good idea to do so.

Cable-TV systems often use frequencies on the cable that are assigned
to non-television services for over-the-air use (e.g. aircraft, ham
band, etc.). If you have loose or unterminated cable connections,
some of the cable-TV signal will "leak" out and can be radiated. This
can cause interference in those other services.

The cable companies usually have "signal leak" detection teams driving
around occasionally, looking for emission from their cable
transmissions which ought not to be present. I've heard of people
who've had their cable company employees arrive at their door, and
insist that their in-home wiring either be fixed or disconnected.

Also, if you don't terminate a splitter port, you'll create an
impedance mismatch at that point, and this can cause a signal
"reflection" within the cable. Depending on the quality of the
splitter (its port-to-port isolation) this reflection can cause
"ghosts" in an analog TV transmission, multipath distortion in analog
FM, and inter-symbol interference (leading to a higher bit-error rate
and possible dropouts) in digital TV.

75-ohm F-connector terminators are cheap and widely available. It's
good practice to use them on all otherwise-unused splitter ports.