25 years ago, my personal finance teacher told me, "always get to know your banker." Of course, there was no internet back then. If you're using a major bank, it's very likely that just having dealt with a couple of live people won't change anything--you'll just sit there while they file the same online forms you could. OTOH, if you have a real business relationship with a higher-up, it could at least speed things up. It's unlikely with rates at historic lows that you'll get much if any interest rate bump based on relationship (unless you're a good enough customer that you have no need for a HELOC).
Just a quick aside--the lower rate (and payments) are nice. But if things go belly-up and you can't pay your credit cards, nobody forecloses on your house. Moreover, with the recent market meltdown, you can easily see how more mortgage debt and less equity can be uglier than it used to be. My general rule for equity loans is to only use them for home improvements. It seems awfully silly to basically refinance a pizza you bought on credit years ago by putting a lien on your house.