If a 3 prong plug w/ a missing ground pin is plugged into a power strip, will it be grounded?

Your device is Not Grounded. The power strip is grounded, but the ground is not connected to the 3rd wire of your device (which will be connected to any exposed metal on your device). Make a new plug with all 3 prongs connected correctly.

Maybe. Depends on the device and the wiring. The three prongs in any residential outlet are hot, nuetral, and ground. Nuetral is supposed to be connected to earth ground. And the third ground pin is an extra path to ground. This extra path is oftentimes connected to metal cases of appliances should a hot wire ever get loose and touch the case. It ensures(or at least makes it more likely) that the metal case will not become hot and possibly shock the user.

Certain devices are not electrically isolated from the AC line. So if the nuetral is properly grounded in the power system the appliance can also be grounded. But if the power wasn't wired up properly(which happens a lot when a do-it-yourself-er wired up the addition to your house, for example), or if the appliance is electrically isolated(usually because there's a transformer between the AC line and the circuit, the circuit or appliance case can be floating, mening it's electrical potential can move about easily. And in this case, it has the potential to rise to unsafe voltages that can either damage the device or shock the user.

Ignore the long answer about neutral and ground being connected (which is true only at the breaker/fuse box) and the case sometimes connected - the latter was only true for 240 volt appliances where the neutral really didn't carry any current and is was banned in the revision of the NEC that began to be enforced at the end of the 1990's

Your device would not be grounded and you need to replace the plug.

NO, it becomes no ground connection.