Would "mein Schatz" be used between platonic male and female friends or is there a romantic connotation?
The common usage of "Mein Schatz" is reserved for people either in a romantic or in a family relationship (most common mother -> child).
Though, you will also hear "Du bist ein Schatz" even when people are only in an acquaintanceship when someone did a very helpful action.
Example 1: You know a person from sports. You see them every week once, but do not have any further activities together. One day you do a favor to them and the person is very thankful. Thus, they say: "Du bist ein Schatz".
Example 2: Someone is having some problems (whatever they are), and they know that you can give them any advice. They ask you, you listen to them and advice them what they can do. Because they are very thankful for your advice they will finish the conversation by "Du bist ein Schatz".
The only condition is, of course, that they like you. If you're in the doghouse such an action would increase your reputation, but they will only say "Thank you".
Last but not least, sometimes very good friends will say "Mein Schatz" to each other, but that's meant in a slight ironic way. ;)
"Mein Schatz" is used for lovers (and sometimes for babies and lapdogs). You wouldn't use it for platonic friends.
In Vienna, some people call their friends "Schatzi". With a little irony.
You can call your friend "mein Lieber" or "meine Liebe". ("lieb" with the meaning of "dear", not "beloved")