Does SQL Server re-create system databases if they are lost/missing?
Answering the initial question

No.

Providing a solution

The procedure of restoring the system databases is explained in the following Microsoft Article:

Reference: Rebuild System Databases (SQL Server 2012)

Prerequisites


Ensure you have a clear documentation of the old system:  


SQL Server Instance Configuration  
Service Packs and Hotfixes  
Current location of database files  



Restore steps


Rebuild the system databases:  


Insert SQL Server 2012 installation media  
Perform a rebuild using the following command:  

Setup /QUIET /ACTION=REBUILDDATABASE /INSTANCENAME=InstanceName /SQLSYSADMINACCOUNTS=accounts [ /SAPWD= StrongPassword ] [ /SQLCOLLATION=CollationName]  

Replace the relevant information with the values for your instance.

Verify that the installation was successful by consulting the setup summary file:  

C:\Program Files\Microsoft SQL Server\110\Setup Bootstrap\Logs

Restore the most recent backups of the system databases: master, msdb, (model):   


When restoring the master database start the SQL Server instance from a DOS prompt with the -m parameter.
Reference: Restore the master Database (Transact-SQL) for more details  
When restoring the msdb database start the SQL Server instance with the Trace Flag 3608:  


  Prevents SQL Server from automatically starting and recovering any database except the master database. Databases will be started and recovered when accessed. Some features, such as snapshot isolation and read committed snapshot, might not work. Use for Moving System Databases and Moving User Databases. Do not use during normal operation.  


Reference: Trace Flags (Transact-SQL)

Rebuild the ressource database:  


Launch SQL Server 2012 setup program from installation media
Click Maintenance and then Repair
Select your Instance
On the Ready to Repair summary page click Repair

Restore your User databases


Please read


  Important Notice
  If you never perform a restore, you will never know if you backup (procedure) works. Test and test again.