Is it possible to add a comment to a bitcoin transaction after it has been sent?
Certainly. It is entirely dependent on the wallet software you are using. Bitcoin transactions do not actually have comments associated with them at all. Any comments or descriptions are local to your wallet software. That means that you can always add a comment to a transaction as it is simply updating an entry in your wallet software.
The Bitcoin core API has no provision for this.
A specific wallet might have provision for this in its API or through a GUI.