You raise a good point, one that I really only ever considered momentarily in passing, namely that feeding the GI tract what it likes so much could be a good thing in itself.
Perhaps, as speculation, much of the immune system benefit of glutamine is not from what reaches the bloodstream but is thanks to supplying the GI tract, which is known to have a lot to do with immunity.
Anyway, if the supplement has not worked for someone despite solid doses such as 10 grams or better yet 10 grams twice per day, and one is still interested, maybe try the idea of the second dosing being only a few hours after the first, so that the cells of the GI tract may already be sated for glutamine, along with the idea of timing this concurrent with high glucose intake. Pretty clearly the most logical time for this is preworkout and either immediately postworkout or in the hour or two after that.
And if that seems to do nothing, then at least it was a given a fair shot, and one might as well then move on to something else.
Well, one other thing to try: If just starting to come down with a cold, try the glutamine protocol with 10,000 IU of Vitamin D (the safe upper limit of daily intake per the most recent literature recommendation.) For me this knocks it out before it even gets rolling.