Time Machine Backup via another Mac? Since I have broken Permissions, which can't be fixed now, because my sudo is broken too, I want to create a Time Machine Backup. Now the problem: both of my USB-Ports are broken.

After some research I found out, you can use your Mac as a hard disk and you can boot a Mac from an external disk, so my idea is to connect the working Mac (Mac A) via FireWire with my broken Mac (Mac B), so I can use the hardware of Mac A with the software of Mac B and create a Time Machine Backup to an external drive.

Since I don't want to risk that Mac A breaks to, I'm asking here, what I need to do different or of this even possible.
Target disk mode turns your Mac with broken USB into a fancy hard drive. 

You can do anything with that data that you could with any working hard drive. You could copy files from or to it, you could change permissions, you could install an os and you could include it in a backup. 

It’s just data on a hard drive shaped like a Mac.