Could you build a cage out of plumbing pipe? Certainly. Would it be worth a damn? Iffy. Should you do it? No.
Pipe is not designed to serve as structural elements, it is designed to contain fluids or gasses at pressure. Pipe can be bent relatively easily (the only easier to bend metal tubing I can think of is EMT - which isn't even designed to hold pressure,) and any column strength it has is accidental.
Structural tubing can come in two flavours - REW (split into HREW and CREW) and DOM/Seamless.
"REW" means "Rolled and Electrically Welded" (H - Hot Rolled, C - Cold Rolled,) and this tubing will show a definite and pronounced "seam" where the edges were butted together and welded. While this can be used for light structural duty, it should be uses where static stresses will be encountered, and the tubing seams carefully placed to avoid rupture under load. If REW tubing fails, it's at the seam - nine times out of ten.
DOM - "Drawn Over Mandrel" is made from a solid, usually round, shape, that is heated and pulled over a shaped and pointed mandrel. The mandrel is sized to provide the ID of the tubing, and it is located within a drawing die. The amount of material used and the size difference between the mandrel and the drawing die determine the wall thickness and strength.
DOM tubing carries the advantage of being seamless, which simplifies fabrication by allowing you to orient the tubing in any direction (since you don't have to watch out for the seam.) DOM can therefore be loaded in nearly any direction that you would normally load tubing, and you don't have to worry about popping the seal - like you would with HREW/CREW.
DOM is also typically made from 4130 Chromium-Molybdenum alloy steel (or something similar - 4140 and other 41xx and 43xx alloys,) which is an alloy blended for weldability and minimal loss of strength in the Heat Affected Zone (HAZ.) Most ferrous alloys experience a severe loss of strength and embrittlement in the HAZ - which is how the various Cr-Mo alloys came to be.
It is still suggested that electrically welded Cr-Mo alloys are heat-treated after welding to reduce hydrogen embrittlement and loss of hardness/strength in the HAZ, but this can also be overcome by gas welding, rather than electrically welding. Gas welding should be done with a "carburising," or slightly acetylene-rich, flame, which works to prevent oxidising of the base metal, and works in much the same manner as welding flux.
I know I've gone into a lot of detail here, but it's important to remember 1*, and when it's yours on the line, you should do everything you can to tilt the odds in your favour. If you can't do it right, save your nickels until you can - it's cheaper in the long run, since you won't place confidence in something that doesn't deserve it.
I'm not trying to be an a$$ like the guys at PoR (I enjoy BillAVista's tech goodies, but I don't get into discussions much there...) but if I'm going to go into detail on something like this, I want you to understand why I'm saying what I'm saying. Blame it on middle and high school - the most common question on examinations was "Explain your answer" - which you were expected to do whether you were right or wrong. Frankly, I don't want to see anything happen to you that can be easily avoided...
5-90
(1* - One A$$ To Risk - especially when it's yours.)