The simple answer to your question is "no." But let's run with the idea a bit and flesh it out some more.
Could a falcon in either a late medieval or Game of Thrones styled fantasy setting be used in any way like an AeroVironment RQ-14 Dragon Eye recon drone? If so, how? If not, why?
I picked that particular UAV for a reason. It's small, small enough to be carried by a single soldier in his/her backpack. Its primary surveillance system is visual and its primary control system lends itself rather well to the fantasy half of this answer.
The Problem: Communication
Falcons are smart little honkers, and with training can become smarter still. But the fundamental problem with using a falcon for pretty much anything other than fetching lunch is communication. A falcon's eyesight is wonderful, but what's the point of that eyesight when what you need to know is
In the gulch 2 km from my launch point and 37.5° north of the setting sun are two battalions of Orcs including two supporting mages and 18 ballista. Well supplied and well rested. They appear to be staging for an advance.
And what the falcon is actually thinking is...
Military engagements, no matter how patterned they may seem, are actually quite chaotic and unpredictable. How to train a falcon to tell the difference between four ninja sneaking through a forest and four skittish deer? How to train the falcon to remember where a previously unknown river is? How to get it to express the idea, "they're over there!"
I'll be completely honest with you. I think all the training in the world would produce a falcon that's good for scouting maybe one thing only. And as soon as you changed valleys, it's worthless.
Unless you forget medieval Europe and stick with fantasy Game of Thrones.
The cool thing about the RQ-14 Dragon Eye is the way it's controlled: the soldier uses a pair of video goggles that let the controlling soldier see what the drone sees in real time. Cool!
Call it fate! Call it luck! Call it Karma! Oh, all right... Call it magic! Whatever hand waving you use to explain it — your soldiers need to see through the falcon's eyes, the need to sense what the falcon senses (especially alarm or alertness) and have the ability to "feed back" commands to direct the falcon. This (IMO) enhances your story because while a Marine will directly control an RQ-14 without argument (unless it's fighting weather conditions... or flak...), the falcon may actually have other ideas (Mouse!) and the rustler must coax the bird to do as needed. The relationship between rustler and bird would need to be very tight (e.g., another trainer would be hard-pressed to control the bird if the primary was inconveniently killed. You know, while he/she was zoned out seeing through the bird's eyes. "Sire, Galadriel sees two battalions of Orcs 2 Km from here about... ARGH!")
So, I think this is a very cool idea, but the simple answer to your question is, IMO, no — no amount of just training will permit a falcon to be a scout to any useful degree before or during a battle.
But if you work with the limitations and shake a little Game of Thrones salt and RQ-14 Dragon Eye pepper onto your story, I think that would be very cool.
P.S.: I've never seen a single episode of GoT, but I just read @Punintended's comment and I see the OP already had the answer I just presented. My apologies to @Punintended for inadvertently making an answer out of his/her comment.