Appetite for the empire was fading by the start of WW1, for many reasons. People were starting to find out more about what was going on, the Labour movement was becoming more powerful and it cost too much. The UK spent 30% o GDP on defence of it but most of the profits went to private individuals or investment companies.
I remember studying this at school the various treaties and agreements at the time are mind numbly complicated, the theory was that binding states together by treaties and accords and ententes peace would be guaranteed. As my history teacher explained it was like a group of mountaineers climbing a steep mountain roping each other together for safety but not attaching the rope to anything at all.
There are all sorts of theories and pet explanations, I remember AJP Taylor explaining one in a talk he gave on TV recorded in the late 50s early 60s. To the French "mobilization" meant sending the boys to the border to look busy earnest and aggressive. To the Germans their plan was based on the use of the railways and "mobilization" meant they were on the move to attack, there was no plan or facility for Germany to send their boys to the border to look busy earnest and aggressive as a bargaining ploy. They were obviously speaking different languages, but even if they spoke the same language they still wouldnt understand what the other was saying.
As far as the question in the OP, I think they would because Belgium had been created as a neutral buffer state with neutrality guaranteed by the British and French, I cant see how they could have got out of that obligation. In any case it would all be over by Christmas, wouldnt it?