Can one get away with straining the seeds off or is it crucial for the pectin content of the jam?

Panfusine, I would not go through the effort of straining the seeds. I make this jam often, and the seeds are not really noticeable... Especially because the jam is chunky, so it kind of all works nicely together. On the other hand, if you are really going for a smooth experience, then I would recommend peeling of the tomatoes as well, because you might feel the skins more than the seeds.

Yes, you can!