Famitracker is extremely dependent on Windows libraries, and porting it to mobile devices would require a complete rewrite, pretty much.

That being said, it is open source, and there's already someone in the process of porting it to Linux. Famitracker's licence requires forks to be open source as well, so perhaps when this port is complete, someone else could use that source to port the program to mobile platforms.

A temporary (albeit perhaps costly) solution to your forgetting ideas before getting home would be to get Sunvox for your mobile device, if it's available at all (I believe it exists for both Android and iOS, so the odds are you'll be able to get it). Granted, it's not an NES tracker, but at least it'll provide you something to write your ideas down, like a notepad of sorts, so you can just transcribe those ideas into Famitracker when you finally get to use your PC at home.

I doubt the idea ever entered your mind, but just in case, I would like to advise against downloading Famitracker on your school's computers, lest bad things happen to you.