Will the unlocked phone 'lock back' to previous service network provider on 'Factory Data Reset' ?

Hello Friends, I'm new to this website. I do apologize if I'm posting my question on a wrong Thread.

My Friend has MTag Phone which was originally on MTS network, unlocked and registered now with other provider - Reliance CDMA (India).

I've logged in with my Google Account and now I'm not getting any option to LOGOUT from my Google Account and keeps on syncing my CONTACTS, PHOTOS, GMAIL ACCOUNT.

Can you help me about the info:
- If I do a 'Factory Data Reset', (SETTINGS> PRIVACY > FACTORY DATA RESET > RESET PHONE) will this

LOCK back to original service provider MTS? Kindly help.

Thanks in advance.