Not exactly.. I think this is what is happening to your brakes: As the pad wears the caliper needs more fluid in it – this is pumped out of the reservior. The reservior is covered by a rubber diaphragm that has convolutions in it so that it can be sucked down into the reservoir as the fluid leaves it. So either your pads are worn enough that the diaphragm is stretched out near its limit, and will slowly draw fluid back out of the caliper – this only happens slowly which is why if you pump it quickly it works; or the small hole that lets air in behind the diaphragm to equalise pressure is blocked.
Bleeding will restore function because you’ll end up adding more fluid. But for a short term fix you can loosen the reservoir cap and let a little air in there. Just don’t operate the brakes when the bike’s upside down if you do that 🙂 Your pads are probably pretty worn yes?
If there’s bubbles in the line (which is why you’d normally bleed) the lever gets pushed out as your brakes heat up.. different thing.