if you're talking about a quantitative leakdown test, the usual gizmos just do a flow measurement indirectly with a pressure drop over an orifice IIRC. And it's predicated on using specific inlet pressure -90 psi from memory. Not that it matters. But you'd want the flow to be stable for the duration of the measurement after the cylinder is filled up and things stabilize. So a bike pump for that does not seem too promising.
If you're talking about just listening for sounds through the intake or exhaust, I suppose it might work but that does not seem too likely either given the greater volume of those 2 systems compared to the pump.
I suppose you could fill up a biggish tank but that'll take forever.
Can't you borrow a portable air tank and have it filled at a friend's?