There's many issues with a tar.gz file. First of all you can say its a very rough equivalent to a zip file under windows.

There's no way to tell (unless you tell us) that the contents of the tar.gz does not contain any files that are generally source codes. By that I mean like anything that has filename extensions such as .c and .h for instance. With those extensions you cannot make N900 run them but you will need them to be compiled. For that to work you will need to install build environment on your N900 which will literally butcher your N900's rootfs if you're willing to do that without researching.

The other factor is that if the files within .tar.gz are precompiled binaries, you'll need to make sure that they actually do work with N900.. any old executable that you randomly find on internet does not equate to being able to run on N900. They need to be compiled as armel.

Now with all that being mentioned, easy chroot is probably an ideal method within N900, it'll be slow and sluggish but in the very least you can have all the compilation tools from scratchbox repository installed inside the chrooted environment which won't butcher your N900's rootfs and definitely would not leave a mess.

As with backtrack CD/DVD.. No it will not work, you will still need to download and install scratchbox environment which is necessary for cross-compiling. Remember your N900 is not equipped with a regular desktop/laptop CPU, it is roughly the same processor as every other handheld devices. The codebase therefore is different from both, making your N900's CPU understand x86's code is like getting you to interpret other languages that you don't know of without any form of assistance in a nutshell.