As long as the blue cloner supports HID copies, it will automatically convert the chip from EM mode to HID mode. I used a blue cloner both to clone a generic EM tag to my xEM, then later on used a different blue cloner (the blue cloner I own doesn’t support HID) to copy my work badge to the same xEM. Struggled with getting a good read for awhile, but it worked with no weirdness and no proxmark once I did get a good read.
I honestly don’t know enough about the different HID models or anything to know offhand if the NExT will work immediately with it, but I’d probably air on the side of yes, if I had to guess.