It would be a fantasticly huge gamble. The potential outcome of a victory would be very tempting, no doubt, because a complete and utter victory resulting in the control of the Sigmas would put Sirius on it's knees. That complete and utter victory would be a really difficult thing to achieve due to the nature of the clouds, however. Their initial rush would be successful because the nearby GMG will slip into the clouds mimiced across the board by the rest as the enemy fleet approaches. GMG has allowed the RM fleet the initial land grab in The Eighty and has allowed the Wilde Fleet rush to pass through in the Nomad War. In both instances both fleets later faced an organized force of numbers eventually annihalating the RM fleet in one and scattering the Wild fleet in the other.
Gallia is a massive force but the tactics would remain the same. GMG would initially dissappear and from then on it will use guerilla warfare tactics and drag the conflict on for many decades. What this means is that Gallia, from then on won't havve full complete control but will always have to factor in a great deal of resources to replace losses or otherwise ultimately have to cecede the territory.
This doesn't even factor in the sudden friendly disposition all the houses will have have for GMG's plight.
I think it might be potentially possible. It would be the largest battlefield in Sirius history and probably the longest war. But it would be a make or break choice for Gallia to attempt it due to the sheer price such a move will cost.