I do not have that "remote color changing" type as .. I mean that's a lot of technology when a simnple ON/OFF is all you need.
I do have a strip I picked up at Radio Shack.. Now so for I've only hooked up a short segement of it for testing but I was warned that if I ran this 12 volt strip off RV power (which in my case can hit 15 volts) it would not last long.. Knowing a bit about electrical design (I've done that) and construction (Same) I went ahead and did not listen to the nay sayers.
As I type the strip is still glowing brightly,, I forget if I installed in NOv, Dec, or Jan. But it was right around the holiday season (2014/5) when I hooked it up in parallel with one of my ceiling lights so it;'s on for 12 hours at least six days a week.. Still going strong.
Yes you can run ;'em off battery power so long as it's a 12 volt model. I would skip the remote controlled ones though. Go for a straightr strip
All Electronics (Google them) has a staright strip for you (I have two of those in a drawer awaiting failure of some other lights.. Converting to LED on a replacement basis.)