If you want it buy it, but be prepared to also shell out for a new battery, if necessary. If you go in with that expectation you won’t be disappointed. Keep in mind that a brand new iPad (sixth generation) is $329.
Thanks for the reply. The iPad is for a 3-year-old who loves watching youtube videos (dirt bikes, trucks, etc.) so I don't really need a later model iPad right now. I can buy a refurbished iPad 3 for $80 on eBay. If I have to spend another $100 on a battery it's no longer a good deal. That's why I'm wondering what the chances are that the battery would be in good condition.
I don't think there is any way to predict the condition of the battery you will receive. I recently acquired a second generation iPad and considered giving it to a 9 year old. But thinking it through, the old iPad no longer runs the current version of iOS. It no longer receives iOS updates. It probably doesn't have good battery life any more. And it's going to be slow compared to newer devices. I decided to get a 6th gen iPad instead. It cost more, yes, but I know the condition and it will last many years.
If you can't do that, then I'd just go with the used iPad. Who cares if the battery is bad? If battery life limits your 3 year old's screen time that might be a good thing. Otherwise, they can use it while connected to a portable power bank that you buy for $10-$20.
IIRC the iPad 2 is pretty sluggish on iOS 9.3.5, and since the 3 also goes up to 9.3.5 (and can't be downgraded unlike the 2), I can't imagine it being much faster as it only has a slightly better CPU. Get a 4 at least if you can, 10.3.3 fares pretty well on that beast. Apple does not service those iPads anymore anyway, so given they are older, a 3rd party battery replacement shouldn't be that costly if you are concerned about that.