Yes, the camera will still record on the new mover media server. The recording happened based on the template associated to the camera(s). The existing recording on the current media server will still be there and can be playback when needed as per the current retention policy of the .smd files on server.
(Let's say you have set the retention period of15days for those cameras, so the recording still can be accessible for 15days even if the camera(s) are moved to the new server.)
Please check the template used on the cameras and status of the device after moving to the new media server.
Thanks,
Jayesh