Coming at this from the point of view of someone who was a hardware technician and specialist PC builder for 15 years? No, its not the best choice.
Second hand hardware is just a crutch, and it is a crutch that will fail, IMHO.
Good news is, hardware is cheap, if you only want simple things. If all you need is something to type on, and maybe peruse the internet a little, then you really don't need to spend much. That is, assuming you are happy with a more desktop-like arrangement.
Given the actual power requirements of word processing (ie they are nothing at all) you could go as crazy as just buying a Raspberry Pi. The cost of it, a keyboard and mouse and all the bits to set it up would be under £70. All you need then is an output of some sort, be it a cheap monitor or even your TV. And an older LCD panel could cost you under £40, if you don't mind something smaller.
Sounds a bit crazy, but if all you want is to write, that will do you grand. You can throw a few extra quid into the keyboard, in fact, to make the experience more pleasant. Your OS and your Office suite would be free, after all!
Sure, you can go in for one of these corporate refurbs, and they can be perfectly decent! But you are, quite frankly, paying for a lot of guff that the average writer has no interest in. Massive hard drive space? XX gigs of RAM? Multicore CPUs? What use are they for typing?
If, however, you want a laptop arrangement? Well, then money is key. Cheap laptops are more or less an oxymoron. As I put it to prospective customers who say they want to spend only a few hundred pounds on a laptop: saying you can buy a laptop for £200 is like saying you can buy a washing machine for £20. Sure, you could, but would you really want a washing machine that cost so little? There is a reason cheap things are cheap, and its not because people want to feel good about giving you a good deal. There is, after all, no such thing as a free lunch.