Certainly. In fact, ADB isn't at all necessary.
First of all, to save you a lot of worries, I will inform you about FlashFire. It's easily the best way to install ROMs and other such things if you do have root. Download it if you have root.
If you don't have root, here's the non-root TWRP method To boot into TWRP differs from phone to phone, so I won't go into it here. I will, however, detail the rest of the process. Make sure the ROM's ZIP file is on the phone.
- Make a Nandroid backup (optional): You should back your phone up in case something goes higgledy piggledy. Go to Backup and choose what partitions to save.
- Wipe The Phone Go back to the TWRP homescreen, select Wipe and then swipe the bar. Your phone (but not it's internal storage) will be completely reset.
- Install the ROM: Go back to the TWRP homescreen and select Install. Navigate to your ROM's zip file and select it. Swipe the bar to begin installing.
- If you have a Google Apps zip, repeat Step 3 with it.
- Reboot your phone.
That's basically how. Phones can be a bit slow on startup for the first time after the flash, but you should be fine. If something does go wrong, install from your Nandroid backup.