Yes, although it depends a bit on the interpretation of subsistence. Degree of practicality varied but it was a legitimate means of providing meat in addition to other forms of hunting.

From The Art of Falconry, Emperor Frederick II, translator's introduction:

...the sport pre-eminently associated in our minds with the Middle Ages is hawking. And, indeed, it owed its existence to conditions of life then prevailing; for in the days when there were only feeble and clumsy guns, or none at all, the only chance of bringing down birds which flew out of the range of arrows was to send a falcon after them.

This was especially true in certain areas and times of the world- for instance, places where Winter meat was hard to come by and fast to escape, or over barren swaths of land where sneaking up just wasn't easy.

From Falconry & Hawking by Phillip Glasier, Third Edition, 1978

...although nowadays in the West it is considered more or less entirely as a sporting activity, this was not its original purpose when it began. Almost certainly, the first person to train a hawk did so because he saw in it an efficient means of catching food for himself. ... This is not to say that the rich and influential were the only people to hunt with hawks; doubtless there were many people among the yeoman classes who flew goshawks and sparrowhawks in order to catch food.

In Le Roman des Deduis by Gace de la Buigne, a 14th century French poet, he mocks falconers who use goshawks (considering them less noble than falcons). He says their personality shortcomings are "...only slightly redeemed by his efficiency in filling the larder", which would fit right in with the goshawk's reputation.

Subsistence hunting using falconry declines steeply in direct correlation with spread and lowered cost of guns, understandably, so when you look at the history it feels like all of the sudden the bottom kind of drops out. Restricted access to the large areas of open land is another major factor for why it isn't nearly as practical today.

The romanticism of falconry practiced by the upper class tends to drown out the use of birds by the lower classes as practical means of acquiring food, but the latter did indeed exist, and is the prevailing theory on why falconry exists at all.