Well, I'm not sure the question can be answered as either/or the way you laid it out. There are a couple of questions I would ask myself in this case:
1) Which is your main or most important strategy for growing the business? Is your strategy focused around marketing and advertising for customer acquisition, or is it more a business development play where you build key connections and get in the front door that way. The answer is different for each business.
2) About this person's connections: business networking is my wheelhouse, and what I tell people is that person's connections have a DEPTH to them that should be known. That is, you go from NEVER MET to ACQUAINTANCE to TRUSTED CONTACT to FRIEND. The later the stage on that scale the more valuable the connection. I find that many people think networking is like accumulating a mailing list of contacts. In other words, they have a bunch of people at the level of ACQUAINTANCE and they think they have "connections". Inquire as to how deep these connections are, so you get the real estimate of the potential value, rather than a bunch of PR on how connected the person is.
3)On the marketing side, ask yourself how important having specific experience in marketing in your field is. In some industries a person can cross over from marketing one type of business to another without requiring much of a re-orientation. In other industries, it might require more specialized experience to be able to grab the ball and run with it. Whether that applies in your case or not, you would know better than I.