I was wondering if it's possible for me to use the tubes in an old CRT TV to build an audio amp (specifically a guitar amp). If not, would I be able to salvage something else (like an old radio) to get reasonably decent results?
Technically, a CRT could be used to perform amplification as it possesses the three things you need to do so: A cathode (in the form of an electron gun), a control grid (grids, actually) and an anode.
There are a bunch of other parts to a CRT that you would ignore or disable.
The thing you won't be able to ignore is the operating voltage. A typical tube intended for audio amplification might operate somewhere in the neighborhood of 200 volts (for a preamp tube like the ubiquitous 12AX7/ECC83) to 400 volts (for a beam power tetrode like 6L6). A typical CRT might operate in the range of 15,000 volts for a little monochrome unit to 30,000 volts for a larger color one. This brings several complications (and safety risks) that are probably not worth the trouble. Most notably, to use the tube for voltage gain, where will you get a load (e.g. output transformer) designed to operate at this voltage?
If you did operate a CRT as an amplifier, another side effect would be that the electrons not striking the anodes would continue on to strike the screen. If you've disabled the deflection coils (which direct the electron beam to different areas of the screen) you will illuminate a bright spot at the center and eventually burn it out.
Some of the tubes used in the audio circuits of radios will be similar to the common ones in commercial guitar amplifiers. Maybe with different heater voltages used in series connections to avoid the need for a heater transformer, e.g. in the so-called AA5 types.
The late Fred Nachbaur ran a website (still maintained in posthumous operation) that included some audio projects using surplus tubes. He had a "thing" for using tubes with odd heater voltages.