I'd take it off.
When you have tiled the wall and come to re-drill it we provide a diamond drill kit which includes the radiator pipe. Its called the BFKMX and has a 16mm core for a radiator (15mm) and then a few 6mm and 8mm to make the holes at the back for the fixings.
Our kits make the drilling very easy to do. Each hole will take less than a minute.
As for the job with the radiator if you can totally remove all the pipework fittings to get back to the "tails" then you can slip a tile over the pipework and it will leave a great finish. If the central heating is isolated or drained down its easier. If not. IE the system is loaded you may have to avoid going that far or use a pipe freezing kit at the point of disconnection.
This is a Cut hole in a tile for a radiator pipe.
Depending on your job will depend on how much "is on view" behind the radiator. Above its clear there is a lot of wall on show so a neat job is critical. The radiator must be completley removed and the tiles placed on the wall. The pipe work or "tails" are then cut into the tile.
Above is the result of drilling a tile for a radiator pipe. Doesnt matter if its ceramic, slate, marble, granite or porcelain. Same thing.
It does involve a reasonable amount of time, prep, plumbing and interference with other systems (IE the central heating) so should be done in conjunction with a plumbing team or by a competent all-rounder.
Arctic do a little pipe freezing kit if the system is loaded. You probably need to freeze each pipe twice. Once on removal. And again on installation. A bit tricky but possible.
The diamond drilling kit for a radiator pipe