Yes, swords are 'root' feeders. But IMO, no you do not have to use in-gravel fertilization for them to thrive.......at least in my experience.
I grew them for years with regular nutrients, until I got tired of them taking over my tanks. One day I just pulled them all(no easy task as their roots had expanded to cover most of the bottom of the tank as well), and took them back to the LFS.
Crypts are supposed to be big root feeders. I grow them well and have never used plant tabs or anything of that genre.
When your new leaves grow in they should become nice and dark green. If after a period of time they start to fade, you can fertilize with regular water table nutrients and they should do fine.
Len