Actually it's my dad's flash that he bought many many moons ago to use with his old Canon T70. I don't have a flash but have borrowed his to try out, but he mentioned that some flashes will send too much voltage down to the camera and can damage the camera. That's the last thing I'd want to happen to my new baby (a 5D Mark II).
The 277T should be fine, as referenced in Photo Strobe Trigger Voltages. If you're still not sure, you could always email Canon support to find out, but a quick Google check shows that it is being used on modern Canon dSLRs.
Yes, if it is an old flash, it is possible that the trigger voltage is around 200V. However, according to some information from Chuck Westfall (Canon USA official), all bodies since the EOS 20D should withstand this voltages (I don't have the link, but you can search Google and it will pop up in one of the many forums).
To be on the safe side, you can get yourself a safe-sync device that decouples the electrical contact between the flash and the body.
Anyway, if you want to be sure about the voltage, you can test with a multimeter. The problem is that most of them have a too-low input impedance so the reading is false. You need one with 10MOhm at least. I just got a cheap DMM from Walmart that was actually able to correctly measure the 190V on my old Sunpak flash, where 2 other meters failed and read around 6V. I know it should be 190V b/c it was confirmed by an industrial FLUKE meter and later on by Sunpak representative.
The Walmart one is from the Automotive shelf and named INNOVA EQUUS 3300. It specifically mentions 10 MegaOhm in big writings on the package.
This post may help: http://forums.dpreview.com/forums/read.asp?forum=1031&message=26638040.
Yes, you can use a 277T on your 5DmkII (the sync voltage was measured at 4.8V, and all Canon dSLR bodies made after the 300D have a sync voltage limit on the hotshoe of 250V), but obviously, you're not going to have e-TTL II, HSS, manual power control, or camera menu control over the flash. See What features should one look for when selecting a flash? for descriptions of those features and why you might want them.
The 277T uses an external sensor (autothyristor) to regulate flash power, so you have to dial in the iso and aperture setting you're using on the camera onto the flash, and then shoot.
See also: the 277T user manual.