Could be my myopic perspective, but I don’t see how using a HELOC as a checking account could provide you any benefit whatsoever. HELOCs take your money, most checking accounts earn you at least a little money.
The only way this would seem to make sense was if you had a HELOC already, then yes, it makes sense to try to pay it down as quickly as possible (all the while not really making a dent in your first mortgage). When it’s paid off, close it.
So, Next in Line, is the gist of this thing that you obtain a HELOC to get it going? If so, then I would consider it a bad idea.