Restore OS then restore apps and data from Time Machine?

If you do step 1 without an erase, you should have a new OS install with all your data and applications. There wouldn't be a need to do step 2.

If you do a full restore from Time Machine, you will be restoring everything, including the OS.

If you do step 1 and do an erase/reinstall, after rebooting normally, use Setup Assistant to restore your data and applications.

Yes, it will work.

Why are you doing this?

You cannot install your Time Machine backups to your friend's computer. He does not own them. This includes the OS. The following will install the original version of macOS that came with the computer. Your friend can then re-download his/her third-party software and reinstall it.

Internet/Network Recovery of El Capitan or Later on a Clean Disk

If possible back up your files before proceeding.

1. Restart the computer. Immediately after the chime hold down the (Command-Option-Shift-R) keys until a globe appears.
2. The Utility Menu will appear in from 5-20 minutes. Be patient.
3. Select Disk Utility and click on the Continue button.
4. When Disk Utility loads select the drive (usually, the out-dented entry) from the side list.
5. Click on the Erase tab in Disk Utility's main window. A panel will drop down.
6. Set the partition scheme to GUID.
7. Set the Format type to APFS (SSDs only) or Mac OS Extended (Journaled.)
8. Click on the Apply button, then click on the Done button when it activates.
9. Quit Disk Utility and return to the Utility Menu.
10. Select Reinstall OS X and click on the Continue button.

Note:

1. To install the version of OS X that was currently installed use Command-Option-R.

2. To install the original factory version when the computer was new use Command-Option-Shift-R.

Step 1 - if you don't erase/reformat the drive before reinstalling the OS, all the data will be there. Do that, then step 2.