I used to only seal around the places where the seam strips intersect with the floor, but in spite of my best efforts I always ended up with at least one leak that I had to track down, and finally I decided that for me (and most people) it is worthwhile to apply seam sealer to the inside of all the seam strips.
Because you have a zipper, it won’t be a big deal if you want to try without seam sealer, although it will be more difficult to apply it inside if you do decide you want to later (but you can apply it to the outside, instead).