To me it seems absolutely like it, yes. For whatever reason, Flies are sophisticated nuisance animals, they got all the perks to be effective in that endeavour. If you signal them it's their life or death, it's even more interesting, prime directive is to dance on your nose by then.

Fortunately, they got a few "bugs in their code" which makes them a bit more controllable, I know of a few very interesting ones:

• Fear of moving fabric:
  Be it a sock or a T-Shirt, once it starts to whirl through the air somewhere near them, they panic. Try and compare, take a solid object (even a fly swatter) or your hand and just whoosh it close by. Often they are back within the blink of an eye, even more annoying now. Try the same with something out of fabric, they will keep 10 times the distance afterwards.
  Possible explanation: Their fly brain interpretes it similar to bird wings, a threat even they take serious.

• Sleep mode in dim light:
  While flies seek out a place to sleep in the light of a single tea candle, you can still see them. Incredibly useful to get rid of flies in small spaces like a caravan or a tent. Possible explanation: They just lack vision, so their only option is to chill at the closest surface.

• Fear of crawling into openings:
  If a fly wakes you up way before your time, build a little cave in front of your face (Think of the entrance to an Igloo). They won't crawl in for the life of them.
  Possible explanation: The ones crawling into the mouth of something often didn't live to pass on their genes.

• Water bottle reflection:
  How to: Fill a clear bottle with water, close the lid and put it up where they have to see it. I have to admit, I long thought of this as being silly and esoteric Mumbo Jumbo, yet after several attempts at it when Flies became unbearably annoying outside, there are clear differences in their behaviour once you put these up. They will still annoy you from angles where they have no line of view to the bottle, so prepare to set up a few.
  Possible explanation: Reflections messing with their vision, esoteric Mumbo Jumbo.

I'd be happy to read some more if you came across something that messes with them, I hate to simply kill or poison them (Don't want fly innards in my living space or poison my surroundings) but to be annoying in revenge is fair game, especially when you get rid of them that way. Btw: how do the salt gun folks deal with the salt being literally everywhere after a shooting spree?

Instinctively, I doubt it. But they can pick up on the air moving around from you trying to swat at it, which is why it's such a pain in the ass to capture to release or kill one. They are able to tell well before they're captured/caught that something is coming for them.

This BU blog entry from 2012 gives a lot of interesting information on the many ways they are able to evade us.

I don't think they can recognize the flyswatter, but they do seem to find a sudden increase in movement around them suspicious. Move slowly and strike from close up.

This happens to me, but with mosquitos. We have an electric tennis racket shaped mosquito killer bought from some random online store.

Whenever I stand up to get that, when I return the mosquitoes are gone. They won't come back until when I put the racket back away from me.

Im thinking they might be detecting the electric charge leaking from that cheap electric racket.

I maintain a silly belief that flies can in fact see a few seconds into the future, and that's how they evade things so deftly.

This is why my family invested in some of those Salt Guns you can use to kill flies. If you're going to be driven crazy, it should at least let you release some steam.

Understand to that time appears differently to Flys. We move in slow motion to them.

As silly as they seem, the anti-fly salt shotguns work super well precisely because you aren't swinging them wildly around, alerting the flies. You can almost poke them with the barrel tip if you move slow, but the actual shot comes too fast to evade.

My experience is YES. They can sense the danger somehow.

I have had much better luck using a cup to trap them. Seems to me that they aren't as likely to fly away when I approach slowly with a cup to trap them inside the cup, then slide a piece of paper or cardboard across the opening and release them outside. Of course only works when they land on a flat surface like a window.

I've noticed this with even fruit flies. I use an electric swatter (in addition to the apple cider vinegar trick) to get at them, and they seem to recognize that something is threatening them. Maybe the electric swatter emits some sort of sound that only they can hear, I don't know. But as soon as I pull that swatter out, they all seem to disappear.

No, they've just made a deal with the devil.