In your situation once the CP enter any Belgian hex Belgium becomes part of the Allies and all of their hexes become Allied controlled. Thus G02 would be Allied controlled.
At the very start of the game the Belgian hexes are neutral. If the CP avoid the Belgian hexes then those would remain neutral.
I too am struggling with hex control, especially as it regards Belgium. This response seems to suggest that the Optional Rules for Belgian neutrality (13.2) is the standard rule. But 11.1 Nation Specific Rules for Belgium state that Belgium begins all scenarios as a member of the Allies (albeit with restrictions about LPs, Artillery and Air Squadrons).
It certainly seems in the Mobile War scenario that Belgium begins neutral, given where the Allied and CP control markers are placed at set-up. If so, and if rule 13.2 is the standard (and Belgium becomes Allied the moment a CP block enters Belgium) what happens to the Allied control markers that were on the French/Belgian border? Do they 'snap' into place around the CP's newly controlled Belgian hex?
Apologies if I have missed something obvious. Loving the game so far though!