After three Months if the oil pump is worn, which it almost certainly is then a lot of oil will be down there, the oil pump is bigger on the return side than the feed side so eventually the oil will be returned to the tank, while this is happening it will be getting thrown around by the flywheels and up the pistons where it will burn and create a lot of smoke, also it will probably be pushed out of the engine breather and make a mess on the bike and the ground.
Anti wet sump vales are fitted to this engine but in BSA's infinite wisdom you have to split the cases to get to it, an easy answer if you regularly leave the bike for long periods is to fit an after-market valve in the oil feed pipe these are available BSA specific which screw straight into the crankcase in place of the original adaptor, failing that drain the cases before starting or put up with the smoke and mess.