No analysis or recommendation for your lawn's unique conditions, just some basics for you to consider:

A dethatcher (power rake) has flail type blades . They are designed to be set just above the soil surface and pull up the organic mater above the soil. The individual flail blades have a great deal of lattitude for side-to-side movement and do a good job of evenly pulling up thatch during a pass. They are not intended to engage the soil. Being flail, they deflect when meeting resistance. In my experience, the use of a power rake for seeding shows results no better than just broadcasting seed, rolling and topdressing.

A verticutter (often erroneously called a slit seeder) has fixed blades which can cut into the soil. Like the power rake the height/depth of the blade can be adjusted. They can be set just of above the soil surface and can do a decent job of removing a majority of thatch, but as their blades are fixed and cannot move side-to-side, they do not remove the thatch as broadly as a power rake, but this can be cured with a second, perpendicular pass if necessary. What a verticutter does excel at is placing seed into furrows created by the blades and, in my experience, with improved seed germination success.

My process is to mow and bag the existing grass to 1". Use a verticutter with the blade set to just above the soil and make one pass to remove the "thatch" and uncover the soil. Rake up and bag the "thatch" using a leaf rake. Broadcast seed (rather than use the drop spreader that comes with the machine). Reset the depth of the blade so that it cuts a 1/8-1/4 inch furrow and make two passes, the second pass at 45 degress to the first. Roll and topdress with a thin layer of peat moss.

Common manufacturers of both power rakes and verticutters are Ryan, Blue Bird and Billy Goat and rent in my area for the same hourly/daily cost. Look for fixed blades to distinguish a verticutter from a power rake's "dethatcher" free swinging flail blades.

Sorry, I just re-read your post. You have a dethatch rake. Disregard prior post. Depending how aggressive you are, the thatch rake can break up the surface of the soil. I've used it that way to spot seed small patches. So yes, your plan would work--but it is a lot of work.