Yes, you will be able to use the weapon, but only after you've researched it.
And yes, intact weapons do give some research benefits.
In order to research plasma pistols or light plasma rifles, an intact specimen is a prerequisite.
Obtaining an intact plasma rifle or heavy plasma rifle allows those weapons to be researched without first researching prerequisite weapons, so you could for example skip researching light plasma rifles entirely, or outfit your heavies with plasma weapons without having to first research regular plasma rifles.
There is also a lower cost to researching advanced plasma weapons if you have a specimen of the weapon you'd like to research.