I assume you mean refurbished ones or ones off non-Apple sites, since the new ones all come with 4GB minumum.
2GB of RAM is barely enough now. I assume you expect the computer to last a while, and 2GB of RAM will be woefully too little very soon.
That said, it'll work fine today for her needs and uses today... but no guarantees about next summer, for example.
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On a related note:
If those are truly her only uses, I strongly recommend considering one of the new Chromebooks (the $199 one is cheap, has lots of storage and outputs, but is a bit noisy with the fan, and the $249 one is really quite nice but very limited on storage... but it uses an SSD instead of a spinning hard disk, and that's a big plus).
They only really work when on WiFi (unless you're looking at stored media files... there aren't really any true apps on them), but... hey, $199 or $249 is a very good price, and even though they only come with 2GB, they're cheap enough that you could buy 4-5 of them over a few years for the price of the lowest-end MBA.
I have the $249 one, and it really is a very MacBook Air-like experience - 80% or more of the MBA for much less money. I also have the real MBA, which I prefer overall because I develop and use apps, but the Chromebook is a very nice option for those who mainly surf/play Flash games (yes, it plays Flash).