Q:

Would we be able to detect signs of life from the contents of a water plume?

Hubble has detected water vapor plumes shooting out of Europa
Wikipedia writes to say 

it is predicted that the outer crust of solid ice is approximately 10–30 km (6–19 mi) thick

Getting to liquid water through ice that thick may not be feasible given contemporary technology. 
Could a hypothetical fly-by probe collect samples from the plume? If life does indeed exist beneath the ice, could we detect it by analyzing this sample?

A:

Simply, it is possible, but whether or not we can build a probe like that is up for discussion.
This geyser occurs when Europa is at it's apoapse around Jupiter due to the weakening of the tidal forces on it's surface. All the pent up pressure under the surface shoots outward as a geyser, reaching heights of up to 125 miles. 
Now, to quote NASA, these plumes jet out of the surface with seven tons of material a second! As it get's higher it will diffuse and slow down slightly, but still, it's a really fast cloud of matter hurtling towards the probe.
Assuming the probe could time it's orbit and altitude to pass through the geyser at the right time, I'm pretty sure it won't be able to survive the impact with a regular design.
However it would be pretty interesting to research ways to accomplish this mission. You could possible use a probe with a heat-shield and a cargo bay. The heat-shield will protect the probe and store the geyser material in the bay. The probe can then dock with a command module in high orbit and study the materials at it's leisure.

