Seems like it would be real slow draining through the cartridge filter air relief valve. The weather has been perfect for a quick drain and refill. Have you considered just buying or renting a submersible pump? Doing a series of 20% drains is not the most efficient way to replace water.
That aside, your plan should work assuming the vacuum hose and the port to which it is connected remain submerged. Pool vacuum hoses are generally not airtight. You should also consider adding a hose bib to your pool plumbing. This will allow you to drain water without using the filters valve.