Some repeaters do not have courtesy tones. We have a Yaesu DR-2 fusion repeater. It has no courtesy tone. It does transmit its callsign in Morse when it has not been keyed up for a while. Apparently Yaesu did not provide for a courtesy tone.
When you mention "connecting" to a repeater the connection is when you transmit then you are disconnected (listening). Some repeater may have long "hang" times. That is, they do not un-key for a period of time. Most do not.
I suggest you visit hamoperator.com for a wealth of Fusion and Wires-X info. There are several Fusion repeaters in the Metro New York area. They are registered with Yaesu and will also allow you to link worldwide. When you connect locally you can get help and advice from local operators.