Generally oil pumps would rather pump air than oil, given the opportunity. If the oil level drops below the level of the top of the gauze in the tank, the pump will suck air through the top of the gauze, rather than the oil surrounding it. I have recently taken out a couple of supply gauzes that had been unmolested these many years, and was astounded by how clogged they were, and yet oil appeared to drain through them. In fact it was only a trickle, and when asked to provide a proper flow - nothing doing. If the oil tank has drained into the engine, you could have been pumping air, until the tank was replenished by the return? Many other makes suffer from wet-sumping, and it is tempting not to refill until after a start as the usual result is oil cascading out of the tank cap or breather, but it is usually better to drain the crankcase first.
On a cold morning you could wait all day for SAE50 to drain down a 1/4" bore pipe by gravity (loss of head), so yes the pipe bore does have an effect. Hence the recommended use of thinner oils in winter. If the pump action is weak or leaky - perhaps at the pump to cover face itself - it will keep itself happy sucking free air. If the ball valves are gummed up, then all action is lost. A hot air gun used with caution might wake it up if the oil has all but solidified in the passageways.
I would remove and clean the filter in the tank, check the air hole in the cap, the unions for cracks or leaks. I would check the the pump itself is functioning by running a feed to it from a separate header tank - e.g. a tin hanging off the handlebars with a length of clear pipe as the feed pipe to the pump, and see if things improve. If no change, it's the pump. If OK, then it's the tank end.
Keep us posted!
Doug