There are a couple considerations regarding the Battle for the Gas Giant.
The first is that enemy activity arrives at 100D. For Jupiter, that's 14.3Mkm. Even for space, that's a Long Way. In TNE, with its 30,000km hex size, that's 475 hexes in range. At 3G, it's a 12 hour trip to the gas giant.
It is fair to say that the electromagnetic and spectral environment surrounding the Gas Giant is powerful enough to effectively blind most any sensor the approaching fleet may have. As soon as the fleet starts to arrive, the SDBs etc orbiting the GG will detect a flurry of anomalous shadows and ghosts on the sensors to provoke the SDBs to "go deep" and wait for them to arrive. They won't all go deep, something will stay up "in the clear" in order to alert the hidden ambushers that the ships are on their way, and when they're close. Could just be sensor satellites.
The next question is really whether the SDBs will truly be hidden as the invading fleet gets closer. I would imagine it would be routine for the fleet to send lead elements to start taking out sensor platforms and such, to try and blind the SDBs. I also assume that there's doctrine to deal with this. They may be able to better probe the GG for the presence of SDBs, perhaps have ships or sensors that will dive deep as well, trying to root them out, trying to get a scale of the threat.
The fleet will be particularly vulnerable during refueling for two reasons. First, they're on well defined courses. They're fueling, and skimming, they're in the higher G field of the planet, and what they are not doing, is janking and jinking and evading. Also, the most vulnerable fleet elements may well be the ones in harms way -- fuel shuttles, tankers, etc. Ships not designed to be shot at, ships without major defenses.
The good news, is that the GG atmosphere is an effectively impenetrable armor for lasers, and particle accelerators, perhaps energy weapons. None of those travel well in atmosphere, much less the thick atmospheres of a GG. This means that the SDBs pretty much "have to surface" before they can engage the fleet. And they'll need lock ons before they can start launching missiles. These could be handed to them from sensor platform, however, assuming there are any left.
Which goes to the next point of how viable are SDBs in this role in the first place. Why not simply just wait in orbit.
The fleet is thirsty, but it's not some dumb herd of horses willing to drink bad water. They'll take their time to suss out the situation. If nothing else, there's some gist of intelligence on the system as to what may be waiting for them.
Finally, the SDBs I think are going to have to be comparable in size to the invading fleet. None of those "400 ton SDBs", not in a big ship universe. If the fleet is bringing 10-20-30K ton battle riders and 100K ton BBs, the SDBs will need to be similar.
Because a key point here is that the SDBs can't fight a delaying action. Obviously it depends on the system structure, but with your generic "GG in the outer system, rocky people worlds in the inner system", any elements from the inner system are a week+ away. The invading fleet has a full week to blast the SDBs to smithereenies and fuel. So, all the SDBs can do is either be powerful enough to prevent the fleet from arriving at all, or sacrifice themselves to degrade the fleet in some way by damaging them, but, inevitably, losing the battle.
The latter suggest a quite strong force guarding the GG (assuming there's only one). Is that really the best place for those forces when they could instead be reinforcing the main worlds which are the "real" potential targets and what you really want to protect? Having an enemy fleet dancing in the outer system is certainly threatening, but if they're not attacking the actual targets of value, are they really actually accomplishing anything? They could pin a defending fleet to be sure, but it's an expensive way to do it.
Now, I can certainly see a value for patrol SDBs, in more a Coast Guard role to keep an eye on pirate, smugglers, and other potential ne'erdowells that may want a free drink, the type of nefarious parties authorities may want to keep tabs on.