Q. Can I use Azure Traffic Manager to balance traffic for FTP/other services?
A. Traffic Manager provides a global DNS service that enables multiple endpoints to be configured, then resolves queries to one of the endpoints based on a number of load balancing methods such as closest, round robin and failover. DNS name resolution is not service specific so a DNS name resolution request would work for any service such as HTTP, HTTPS, FTP, SFTP, etc. However, Traffic Manager has to be smart enough to monitor if endpoints are available so that resolution requests are only resolved to endpoints that are available.
Currently Traffic Manager supports two protocols for monitoring: HTTP and HTTPS. A custom port and path can be specified, but the actual monitor has to occur over one of the two aforementioned protocols. So if you wanted to use Traffic Manager to distribute traffic for non HTTP/HTTPS traffic, you would still need to enable HTTP or HTTPS on the endpoints of the service to allow Traffic Manager probing to occur.
In your example, if you wish to use Traffic Manager to distribute traffic to FTP servers you would also need to have HTTP or HTTPS running on the FTP servers to enable Traffic Manager to check the servers are available.