I am planning to use Google Places API in order to create an address autocomplete in my web site. My question is about whether my requirements are possible using Google Plac
Google Places will help your user autocomplete their address as Sean Mickey describes:
The id in that response is going to be for their street address, not for the city. So it's not going to be useful the way you want. If you want to match on city, you need to store the name of the city (if you want you can create your own id table).
Think about how you want to implement location search in your database:
If you choose to search by distance, you should also be storing the Latitude and Longitude that Google Places gives you back when the user enters their address. You also need to read up on how to do spatial search in your database (especially geodist).