Asking a Connection to Put in a Good Word

Late last week I had a first round interview (virtual) and because of the nature of the platform (and the name of my interviewer) I didn't get a chance to send a thank you email to the VP (tried searching LinkedIn, assumed he didn't have it). About a half a week later I miraculously found him (he had a unique name) through one of my connections' posts on LinkedIn (we aren't particularly close but I met this person 3 years ago and really impressed him, he is NOT IN BANKING). My connection is not in the IB side of the firm but is still a pretty high figure within the retail side of the bank and they work together professionally . Do you think it's a good idea for me to message my connection and ask him to put in a good word, or do you think at this point it's pretty much useless. I'm not sure how much this VP would be able to push me along in the process