Not quite.
You connect your phone to your PC via USB, boot the phone into Fastboot Mode, and then you execute fastboot boot twrp.img (or whatever the filename is) in a command line on the PC.
This will then boot TWRP on the phone without you having to install it. Nothing will change on the phone, as long as you keep System read-only in TWRP (important!) …
You can then use TWRP on the phone to backup the partitions …
Here’s a little something in case you’re interested …