Whether invited or not would be irrelevant to the principle that Germany must not control the Belgian Channel ports. "If Belgium took the more drastic step of allying with the Central Powers" means that Belgium has joined the Central Powers as an ally in the war and after it. For Britain, Belgium must not be in the Central Powers under any circumstance - any nonsense from Berlin that the alliance would end with the defeat of France would presumably be treated as an untruth, as once France was defeated Germany would be free to do whatever it wished with both France and Belgium.
So if Belgium is invaded by France and because of that Belgium accepts the help of the only power willing to give it - Germany, than Brittain will attack Germany and Belgium. Sorry but thats simply insane.
1. The channel ports wont be in german hands. They will be in belgian hands. If there will be german forces in Belgium they will be busy fighting the french in the southern part of the country not occupying allied territory.
2. Brittains declaration of neutering the channel has not been butterflied. Meaning if Germany tries to move ships to Antwerp and starts fighting in the channel than yes, Brittain will declare war. However if Germany formerly accepted Brittains declaration I dont see why they would start to ignore it in this situation and thus provoking war with London.
3. Germany will be busy throwing everything he can spare at the russians in the east. Im no expert of the military questions however I doubt how much troops they will have available to help Belgium and how much troops they are willing to move in to the area for this goal. Because without driving the french from Belgium they wont be near the channel ports and might well be cut off from not french occupied Belgium. However liberating Belgium means a much longer front and that means significant forces removed from the east. Im not sure if in a situation like this Germany would not decide its better not to exert itself too much on behalf of Belgium in order to keep the western front short. Cold but its a possibility.