Does Time Machine fail gracefully if I eject the backup disk during a backup? I'm using an external USB HDD as my Time Machine backup disk for my MacBook. I have it plugged in as long as I'm working at my desk. I don't have it with me when I take the laptop somewhere else. However, I'm afraid that at some point I'm going to need to go to a meeting or something that requires me to bring my laptop, which means I'll have to unplug my backup disk. What if I can't wait for it to finish because a client is here? Time is money, you know!

My question for you is whether Time Machine fails gracefully if I do this while a backup is running. And I'm not talking unsafe unplugging; I would use the "eject" function.

Normally, I would try something like this myself, but a lot is at stake here if it fails!
In your assumption of properly ejecting the drive first, there'll be no issues: the partial backup will even be kept so that files which were already copied during this partial backup and you didn't change in the meanwhile won't have to be copied again.