I would say its possible, maybe not to build one, but to get one its certainly possible. Try your luck on craigslist for a low end or budget gaming PC.
CSGO is not hard to run, as long as it has a midrange graphics card from the past 6 years, and a quad core or fast dual core you should be able to get playable FPS. this is assuming you dont need peripherals.
Find PC in your budget, look up what fps others get with similar components. happy hunting.