If your attempts at vacuum bagging are like mine, even with a pump going, you spend a fair while chasing leaks before the bag will suck down. I even made up an adapter to use a vacuum cleaner to draw the bag down initially, as a normal pump takes forever.
I can't imagine doing it with a manual pump, and by the look of it, your pump needs to be drawn up to pull a vacuum, which looks a lot harder than if you were pushing down on the pump.
While I am at it, the level of vacuum you are going to be playing with, a gas cylinder won't hold much. I ended up using 5 metres of 100mm PVC tube as a reservoir, so its probably similar, and it makes a difference, but that's with an electric pump and prevents it cycling as much.
Vacuum pumps aren't that expensive off of ebay, and make it so much easier, although my attempts haven't always been that successful either