I have a few clients who have GP and Management Reporter installed on a server other than SQL. One of the reasons is so that when an update is installed and the server needs to be rebooted, SQL itself does not.
GP itself does not actually require a server (other than the SQL Server) so any update could be done from a desktop client machine somewhere on the local network without a reboot of the SQL server being needed.
Your DBA is right that two instances of SQL could potentially compete for resources, but each instance could be limited to a certain amount of RAM that it can't exceed and as long as the two combined are less than the total in the machine (allowing for what the OS and any other applications need) there should not be a problem.
If you are going to combine GP with another systems SQL Server then you will need to make sure that other system can use the server collation which GP requires (SQL_Latin1_General_CP1_CI_AS) or they cannot be combined; and GP cannot have it's collation changed.
Management Reporter does have a server side component which could require co-ordinating when upgraded if a reboot is required.
Ian