From the description, you should chase it. Why? You said, if you make it, he will pay you off. Putting a dollar in to stack him for 3 more easily gives us the odds
to try and catch. Plus, we have a gutshot and probably any J also.
The answer to your question is... You should chase the FD to the river, if you are getting the right pot odds
. You aren't getting them here, but you are saying we are getting the implied odds to chase it, so it is basically the same thing.