It does! We did this, oh must be 5 years ago. I only wish I had Turner Classic Movies. That was about all I watched with cable. $150 per month was too much for one channel. Lol.
You should look into SLING TV.
On Sling, TCM is a $5 upgrade to either of SLING.TV’s base packages. (Sling has two different base packages. $25 & $30 IIRC) That same five dollar upgrade also delivers The Film Detective, another channel delivering curated film content quite similar to TCM.