For £20, to me it would seem silly not too.
Just replace any parts that could have perished, certainly the o-ring and the starting pump (will cost under £10 for both). Remember to lubricate the o-ring every now and then.
Obviously clean the impeller and make sure there's nothing wrong with it like cracks.
I'm skeptical about people who say Fluvals are notorious for leaking. 04 range had a very bad run years ago at the start, but otherwise the 05 range seem to be just as reliable as similarly priced filters tbh. All brands will have an odd bad filter/run every now and then and people can get really annoyed with that brand when they get one. I'd speculate more popular filter/been around for longer = more people own them = increased chance of someone complaining about a bad one. Wherever you go or whoever you ask people will have different experiences. Read around here and you'll find some people really bitter towards Fluval, most people have no problems whatsoever.
Look around and you will also find threads about issues with other manufacturers like Tetra, but loads others who have no trouble whatsoever with them.
Worst case scenario if the filter is really old and abused you may have to an aquastop valve and/or impeller as well.
It would be the same with any other brand second hand filter.
If you paid more for a used Eheim chances of its conditions being good would be better, but you'd still need to replace perishables for good measure.
£20 is excellent for a 305, mine was £60 new and it's been fantastic.