No, the connect clip has only a USB connection for charging (and firmware updates). There is a EduMic that is targeted at educators for children who wear hearing aids - that has an audio line level input but not, as far as I can tell, a microphone level input. You could probably use a microphone with an appropriate amplifier with the output going to the line-level input.
https://www.oticon.com/solutions/for-children/classroom-hearing-solutions#oticonedumic
Both the ConnectClip and the EduMic have microphone arrays that are directional. You might be able to use the ConnectClip as a remote microphone as long as it was oriented correctly. When worn, the lapel clip is rotated such that the microphone “line” is oriented up.
However, my experience with a ConnectClip using it as the microphone part of a “headset” with an office Cisco VOIP phone resulted in the pickup of lots of ambient room noise besides my voice. I was asked to mute it so it wasn’t useful for conference calls. My OPN S 1 hearing aids are the other part of the headset.
I can’t comment on any possible latency issue and I don’t see a specification in the technical data sheet.