No, it is not as simple as pay your mortgage with a HELOC and you will save money. There is a strategy to make it work. What I talk about below is based on using a HELOC to pay off your mortgage.
The HELOC strategy does work as long as you have positive cash flow each month and you put all that positive cash flow to the HELOC. Instead of keeping your money in a checking/savings account you put that money to work to keep the daily balance of the HELOC as low as you can for as long as you can since interest is calculated on daily balance. All expenses come out of it and ALL income goes into it applying all the positive cash flow to the HELOC balance. Every time you get a pay check, you make a HELOC payment. So if you get paid weekly, you are making a weekly payment to the HELOC dropping that daily balance each time. It will go up and down as you pay expenses and make payments so there is a strategy to timing of those events to maximize the effect.
Yes you can just make those same payments to a regular mortgage but I don't think anyone would be comfortable using all their "savings" each month to make an extra mortgage payment. That's one of the advantages of using a HELOC because if something comes up you still have access to that money. Once you make a mortgage payment say good bye to that money.
For this to work, you absolutely need positive cash flow and keep to your budget to keep that positive cash flow so you can put it to work to pay down the principle of the HELOC lowering the amount of interest you owe. It could be $300 or it could be $3000 in positive cash flow but if you put it all to the HELOC it will work. Of course the bigger your cash flow the faster your pay down gets. The HELOC gives you flexibility a mortgage won't but you have to be disciplined with your budget. This won't work for everyone.
Side note: not evident from above but because you are replacing your mortgage with your HELOC it is assumed that the amount of what your mortgage payment was would be applied to a HELOC payment. Add in the positive cash flow being applied and you are dropping the principle faster.
Wow, that post was a lot longer than I expected. Sorry for the long windedness.
Aloha, Ho'okani