That really would be jumping out of the frying pan and into the fire. The airline (both BA and the industry generally) is already on its knees through no fault of its own. Industrial action at the moment (i.e. while very few flights are operating) would be largely symbolic. However, to subject the travelling public to further disruption once some semblance of normality has been restored probably wouldn't be well received. I would be spitting feathers if my future travel plans were jeopardised due to strikes or work to rule or whatever. I have a lot of sympathy with BA staff as things stand but to go on strike (again) would be pushing it. The union really would be shooting itself and its members in the foot if it goes down this road.
As an aside, can you actually / legally go on strike while furloughed?