I had a similar question about mushrooms that were grown in a rye medium; if they would be gluten-free or not. I e-mailed several professors at UT Austin and they all responded with a longer version of I don't know.
I did some research on my own and discovered that the mushrooms actually grow on top of the rye and do not root at all, so they are considered gluten free with a risk of cross-contamination.
As for plants that actually grow through the soil and absorb from the soil they might get some gluten in there, but as long as the plant itself does not contain gluten the amount should be too minute to tell.

However, everyone's tolerance level is different and if you have a reaction to something, that's a good reason to not eat it anymore.

Hello, I was just diagnosed last week with Celiac...and I feel overwhelmed with my grocery list....I wonder if it OK to eat beef, and poultry that the animals were 'grain' fed?

I was wondering too if animals fed on feeds with gluten are ok or not to eat. So far I have been told lots of different answers. I am unsure about Strawberries now - are they safe to eat or not. There really needs to be a place with safe information for Celiacs to get info about this stuff, and the stores own label don't have to have allergy advice about this which is wrong! I can't even buy a packet of peanuts from my local store because I've been told they are packed in a factory with gluten/wheat! We need clearer allergy advice about this.