According to a baking book (How to Make Sourdough - Emmanuel Hadjiandreou) I have, the answer is yes. He shows a bunch of starters that he created with bases that include barley, chickpea, oats, quinoa and several more.
I would suggest you give it a try by starting with, perhaps, 50 grams Ischia (made with flour, I assume), 25 grams water, 25 grams your new grain. Let it ferment for a few hours.
Discard half and then feed it again with 25 grams of your new grain, 25 grams of water.
By the time you do it 6 times, for example, the original flour (the original 50 grams of Ischia was 25 grams flour + 25 grams water), it will be down to 1/2 * 1/2 * 1/2 * 1/2 *1/2 * 1/2 = 1/64 of the 25 grams = .4 grams of flour (not material) and 24.6 grams of your new grain.
Assume it does things similar to Ischia - bubbles and grows and roughly doubles in size, then you have a gluten free starter.
I can't tell you how well it works only that it should be possible.