VCR coax out to SDI?
 

Does this work?

Looking to go coax out from VCR to SDI>HDMI converter.

No, Stay away from HDMI.
No one can answer the rest of your question unless you post the exact hardware model numbers, Some refer to BNC as SDI which is only half true, So we don't know what you are talking about.

Wait, why stay away from HDMI? This is the first I've ever heard someone suggesting to stay away from HDMI.

If you are reading a lot you will find out I'm one of the few that worked with another output other than USB. But yes I'm the first one in your post to suggest stay away from HDMI for capturing if that's what you are referring to. Now [give] more details to get answers [to your] post.

I'm really not following.
Back up.
What exactly are you doing? And with what exact hardware?

HDMI is only good for HD capturing. Not SD (VHS, etc).

I would advise you to stay with HDMI.
It is the best way to plug-in and watch.

Please give us more details to help you better.