It did, but it was awkward.

Analog cable channels were on a wider range of frequencies than regular TV (radio broadcast) channels. So the VCR's tuner had to be "cable ready".

Some cable channels, especially premium channels, were "scrambled", which meant you needed a cable box to tune them. So the VCR, by itself, could only record the basic channels that came with all cable packages. To record something from a movie channel (HBO, Showtime, etc.), you needed the cable box to tune it in and provide an unscrambled signal to your VCR.

And that meant the cable box needed to be set to the correct channel at the time the VCR woke up and started recording. The simple method was to leave it on the correct channel, but that was tedious and error prone. As I recall, there were also VCRs that could send a command to the cable box to turn it on (emulating the cable box remote) and set the channel, but you had to set that up.

Later, when digital cable came along, you needed the cable box involved for every recording because the channels were no longer coming over the wire in a format that the VCR could tune in.

So yeah, you could do it, but it was a pain.

I was probably still using recordable VCRs when I had cable--though it was probably still composite video/audio input. But at some point I started using TiVo. Don't remember the whole tech evolution.