I've attached a picture of my computer....all aesthetics aside, cause yeah I realize it's not the prettiest and right now it's dusty as hell, but the point I'm getting at is it's watercooled, CPU and GPU and is completely LAN Portable...infact I go to a LAN once a month because my friends hold one once a month at the local church here.
It's easy to build it into your computer assuming you have a full tower case. Those two fans on top are for my radiator. My radiator is a few inches below those fans attached to the top of the case (which of course had to be modded)
You don't have to buy a pre-made internal setup to have an internal setup inwhich you gotta carry a rad around...infact I've rarely seen anyone actually have their rad seperated, and that's generally when people use huge *** rads.
I'm actually using a heatercore from a car. 2-302 1977 chevette heatercore I believe is all the technical info which is the one a lot of the water cooling community uses as they are more effective than radiators that use simple copper tubing winding around.
Theres instructions on how to mod your own heatercore, so you could essentially go to autozone, pick one up for about $25 and mod away.
And yeah as for draining, no you don't have to drain anything to simply move it...just make sure you aren't tossing around your computer or have crappy seals around the tubings and you'll be fine.