I think they will probably grow, although it will be slower. Many plants need iron so if you get a fertiliser make sure it has iron in it - and no phosphates. From what I understand, phosphates will encourage algae growth.
I have some chelated iron donated to me by Cees, and I've made up a very diluted solution which I use to dose the tank daily - just one drop a day. I do this in all the tanks, including the ones with only gravel and UG filters and the plants are growing slowly.
Cheers