do I have to back my macbook air

Do you have a large enough USB flash drive? You can use it to back up the essential info with Time Machine or simply copy/paste the files that are important to you.

Back up your Mac with Time Machine - Apple Support

Is it necessary to back up?

Only if you care about the information it contains. Otherwise, no.

Put another way, if you do not back up your Mac, then the prospect of permanently losing all the information on it does not concern you. That fact is not related to any need to get it serviced.

Absolutely it is required to backup your data. Apple is not responsible for safekeeping of your data. If your data is important to you it needs to be regularly backed up.