I wouldn't say that it's common, but it does happen. Here are some examples:
- Musaigen no Phantom World had a PV in Jan 2014, which preceded the announcement of its anime in Aug 2015. Likewise, Kyoukai no Kanata had a PV some time in 2012, prior to the announcement of its anime in Apr 2013. I think the same thing happened with Free! / High Speed!. However, all of these are published by Kyoto Animation's in-house publishing division (KA Esma Bunko), so they may well have had not-yet-publicized plans for these works by the time they put the PVs out.
- Heavy Object, Intellectual Village no Zashiki Warashi, and some other Kamachi LNs showed up in a Sep 2014 PV of Kamachi's various works (the best known of which is, of course, A Certain Magical Index). Of the non-Index works, only Heavy Object has been animated, and it was not announced until a month later (though, again, it was presumably in planning at the time).
But after a fair bit of searching, I didn't turn up any other properly-animated PVs (rather than just videos with static images wooshing around the screen). I find this unsurprising: for a properly-animated PV, you need a proper animation studio, and without a pre-existing relationship with a studio to produce material for the franchise in question, a PV is probably unlikely to happen.
So why do these few examples even exist in the first place?
The case of Kyoto Animation is unusual, in that they have a light novel publishing house as a subsidiary (or something; I'm not sure what the exact business relationship is). Naturally, this provides KA Esma Bunko with ready access to an animation studio. As far as I know, KyoAni is the only animation studio with this kind of very tight-knit relationship with a light novel publisher.
In the other two cases - Okitegami Kyouko and the various Kamachi things - the animation studio connection comes through the studios in question (Shaft and J.C.Staff) having already animated other cash cows by the same authors (Monogatari and Index, respectively). There aren't very many other authors in the same position (existing animated cash cow + high productivity on other light novel series); the only one who comes to mind off the top of my head is Narita Ryohgo (Durarara!!, Baccano!), and I didn't find any PVs for any of his other stuff.