I've done it and actually won a beer competition in the "specialty" category with that beer!
It was actually a mistake, though. I made an "Arrogant Bastard" clone. I totally bagged up my efficiency, and got something like 60%. My OG was something like 1.070 instead of my intended OG. The beer was good, but definitely not an AB clone. It was a bit harsh at first, but I knew it would age well (but be less hoppy), so I bottled two gallons and aged 3 gallons on oak chips. It took the oak FAST, and so it was over-oaked as well.
Uh-oh! Anyway, I bottled it and 6 months later it so fantastic you can't believe it. The oak faded a lot, but the beer was rich and just unbelievably good. So I entered in a competition as an "oaked Imperial Amber ale".
It was great.
I do have a point here! Oaking usually requires a "big"-ish beer. The type of oak matters. French oak, medium toast, is a pretty good bet while American oak can be mush harsher and aggressive. The lighter oaks have vanilla-ish flavors, while dark oak can be very tannic. It's a bit tough to balance the tannins of the oak with a less-than-flavorful beer, so that's why you see it most commonly in stouts and other big complex beers. If you can manage to use a lighter toast oak and only oak a short time, as well as let it age a bit, you can make a very nice amber with oak. The hops fade with age, though, so you may want to redry hop if you want a hoppy finish, or you could simply let the oak be the dominant flavor with the caramel flavor of the crystal malt.