My understanding is this method is probably more beneficial for paying off student loans especially if you have multiple accounts. You could even argue going after the smaller interest/principal accounts just to increase your cashflow position every time an account is paid. You'd probably save more money by paying towards the higher interest loans, but by using the LOC to pay in chunks that you could pay off in a few months, you could seriously speed up your cashflow positions. Kind of like Dave Ramsey's snowballing, but in an accelerated fashion.
If using this method for multiple amortized loans, this method works to save you money in the following ways (despite interest on a HELOC or any LOC):
1) By paying in chunks and paying off an account, you gain that cash flow that was used to make monthly payments. You gain it back quicker than regular monthly payments (towards the principal as well) from your monthly cashflow.
2) By paying in chunks, you move down the amortization schedule towards higher principal payments.
I could see paying off a mortgage this way as well, but you just have to be aware of where you are in the amortization schedule, and how much you save by moving down the amortization schedule as opposed to the interest you'd pay on the balance you transfer to the LOC.