Based on my experience this morning, I would have to say the answer to your question is “No”.
I got a HELOC with B of A in 2003, when my condo was appraised at about 35% more than it is worth now. I spent part of what was available to me, then locked the rate on that portion that I had borrowed (at 6.5%, when the adjustable rate would have been just 4.25%, but is now around 7.75%). I set up an automatic payment plan where my monthly payments were just deducted from my checking account.
So, today I called their customer service line to tell them that I would like to start making additional payments to pay down the principle. Before she would make the transfer she wanted to know if I was aware that I had X amount of dollars available!!! and for a limited time only, any money I borrowed would only be charged 6.25%!!!! until March of 2008!!!
What part of “paying down principle” didn’t she get? Why would I go from wanting to pay down my loan to wanting borrow even more? I guess some people would find 4 months of 6.25% interest too hard to resist.
And getting back to your question, if I did decide to borrow the X amount of dollars available to me, I would certainly be upside down, owing more than I could sell my condo for.