I was under the impression the limitation was on what the dwarves could eat/grow themselves. So unless trees are edible, I don't really see the problem there. Besides, as far as importing alcohol goes, it tends to get low priority if you don't explicitly ask for it or if you request a lot of other heavy stuff (giant animals, ore, or lots of metal bars for example.)
Of course a further requirement would have to be no actively requesting it; you can buy what they bring For supply and productivity's sake, but more for the latter, but can't go out of your way to request it. For example, a caravan from home brought 6 barrels of booze one year, and 7 another, and 4 the next, that's your booze from those caravans. And with a moderate-to-large population such a meager supply won't last long (hell they probably wouldn't last more than a season, if that long, if you had say 65 dwarves.) Same goes for the other caravans. By not requesting it, it'd be an unreliable supplement at best, especially if you import lots of animals, ore, stone, and metal to take up space on the carts/animals.
Thsis would also require you to maintain a specific population to make sure supply is too scarce from caravans to be reliable without other booze sources. Between mead, imports, and fermented milk that should be enough to at least take care of most of the fort, but a water source would still be needed since dwarves are sponges for booze and the supply will dry up rapidly with a moderate population.
I'm kinda ranting/repeating myself, but still. Trees aren't food so who cares about them?