I've seen a few, salt water guys often use macro algea. You need a light down there to make it grow. Get some fast growing stuff like whisteria, or hornwort and it can really help with nitrates.
You don't even need a sump if you want plants. I used to cram wisteria, and cabomba in my ten gallon and it helped a ton with water parameters. Never did a waterchange for nitrate removal.
You can absolutely put plants in your sump. As mentioned, you will need a light. Get something that grows really fast. If you were to set up a full refugium, you could even breed some small shrimp and blackworms down there as well.
hey just so you know I'm pretty sure plants are supposed to have a dark period. I think 18 hours is supposed to be the longest photoperiod that is beneficial to plants