Hello Zeetwo,
Moving it should not cause any problems. If the radiator is under a window now & won't be later, your room may heat noticeably differently. You'll still have the same BTU/hr emitted, but the convection pattern will change, heading toward the window.
A few things of which to be aware:
A) Keep the vent on the same side that it is now- opposite the pipe. If you put the pipe on the same side, the radiator will heat in a diagonal from corner to corner. Only the part under the imaginary diagonal line will heat.
B) Since it is a one-pipe system, check the pitch of the radiator and of the piping before disconnecting. When you reinstall, be sure to maintain about the same pitch. Over or under pitched pipes or unit will cause loud banging or maybe even lockups.
C) Be very careful moving the unit. The sections are connected by push nipples.
If the unit is mishandled, the push nipples may start leaking. Tapered push nipples require more careful handling than threaded. (If you see draw rods between sections, you have tapered push nipples.) Replacements are available for all radiators.
D) Be certain that the floor and supports where the unit will end up are suitable for the weight. You can calculate the weight by measuring the unit, counting the sections and columns per section. Many on-line charts will show the weight.
Suggestion- Try to get the radiator feet above joists or a header. I recently had one where the feet were between joists. Physics dictated that the center joist took all of the weight and finally broke it. (100+ year old building, but broken is broken) When you see cracks in bathroom floor tile near a radiator, it's often because the subfloor sagged because the radiator feet are between joists.
E) The joint compound in the photos looks like it might be old style linseed oil based, If the fittings don't come apart easily, try running the heat to get them warm first.
If that fails, suing fire safety precautions for the surrounding wood, a carefully used torch on the fitting will do the job. The fitting will expand. While it's warm, loosen the pipe nipple. On the happy side, none of the fittings in the photos look to be cast, so they won't shatter when you wrench on them.
F) If you have to add pipe, although copper is easier & less expensive than threading new iron pipe, there is a lot of controversy about using copper on steam systems. Personally, I've never done it. It was not legal when I apprenticed & got my heating license, but may be now. Perhaps an article or post at Heating Help Com will give you both sides of the argument.
G) There is a good chance that moving the unit will cause debris to loosen & eventually clog the vent. This is no big problem. Most can be opened for cleaning.
G) When you unhook it, some rust water will come out of the unit and pipes. Be sure anything that will be damaged is covered.
Enjoy Your Project & New Bath!
Paul