I've read the only issue is wasting of media as the carbon would be used up before the gfo if you mix them. Of course the other issue is it's my understanding that you want the carbon packed tight and the gfo to tumble so mixing could be less efficient. Not sure what kind of reactor you have, but if you have reactor filters perhaps you could tumble the gfo in the bottom and then in between put a filter and pack the the carbon tight at the top. This way you could easily change out the carbon and leave the gfo. Of course a phosphate test would be wise to see if it's even necessary to run gfo on a frag tank, assuming nutrients would be quite low anyways. Furthermore, I'm not sure it would even pull out silicates as that is what feeds diatoms. Also, if it is coming from the eggcrate, I would assume the diatom bloom would be brief and probably shouldn't be a concern as they will disappear in a week or two and is naturally part of the cycle.
This coming from 6 months in the hobby, albeit with a lot of research.