If the aligator clip is attatched by wire to the end of the 'screwdriver end', then yes. You use the pointed end to lift up the CRT rubber cap to discharge the CRT. The clip is supposed to be on something grounded e.g. the iMac frame. I always suggest having the machine off 10 minutes before opening it anyways because they tend to discharge properly 90% of the time, but the other 10% is why you do it. And for safety measures, you should always discharge a CRT before working with it or the power/analog boards that are attributed to it.
MacBook 2GHz Intel Core 2 Duo w/ 2GB DDR2 RAM & 120GB SATA 5400RPM HDD
Canon Rebel XTI
Google Cr-48 Beta Laptop