The GE link bulbs which come in a set with the link hub ( The little white square that plugs into the wall) come pre-paired with that hub. So that should work straight out of the box with it.
That said, I haven’t heard anything about a GE link firmware update being available. I know that GE has said that they are going to do one to solve the drop off problem, but I haven’t seen anything that says it is actually available.
After that, Ray is correct, the Phillips Hue bridge Will not be able to do an update for the GE link bulbs. They can only update Phillips hue bulbs.
As far as the drop off problem, that can occur whether the GE link bulbs are connected directly to the SmartThings hub, or through the Phillips hue bridge. You can find a lot of comments on other boards where people just have the Hue bridge about the yellow ! Next to GE link below bulbs when they drop off.
I also wanted to add that there is a new problem turning up in the Amazon reviews for the GE Link hub, which is that it is no longer being updated it all, as it was actually manufactured specifically for wink. (The separate wink hub is more up-to-date.) so if someone only owns the GE link hub it is possible that they could buy newer GE link bulbs that would not work with that hub. Apparently that is what wink support is now telling people. Look for reviews from March 2016 and newer.
That’s an entirely separate issue, but it’s the only recent reference I’ve seen to firmware and the GE link bulbs.