Here's my nightmare scenario:
Me: Okay, there are three guards aiming guns at you. You can tell you have just half a second to do something before they cut loose.
P1: OK, I shoot the first one with my SMG.
Me: Okay, single shot or burst or full auto?
P1: Lemme see, lemme check my attack ratings...*researches, does math*
Everyone Else: *waits*
P1: Lets do a burst
Me: OK, that's a (modifier), their DR is (X) so that's 1 Edge to you. Speaking of Edge, would you like to use any on the attack before you roll?
P1: Wait, what can I do with that again?
Me, probably: Take a look at the cheat sheet I printed up for you.
P1: Oh yeah.
P2: Oh, don't forget you have Qualities that might help too.
P1: Oh yeah!
P3: Oh and some of your cyberware and gear too.
P1: I didn't write that down, hang on, I think I have something that will help, let me look that up.
Everyone Else: *Waits for book to load to tablet, searching and scrolling. Other players start to do the same to try to get through this part*
Me: Okay, so next round you should be ready for that. Let's pick one and go.
P1: I'm almost there. One quick sec.
P2: Found it, page 211, (quotes gear rule), oh no wait, that's no help.
P4: *Makes snoring noise*
P1: Yeah, I've got nothing helpful. Let's just roll.
(We do)
Me: Okay that 2 net hits. Do you want to spend any Edge now?
P1: Hmm...
Me: *Dies inside*
That's more or less my expectation of what the first couple encounters will be like, too.
However, based on similar systems in other games, I suspect the encounter flow will smooth out pretty quickly.
Most Edge gains are going to be pretty straight forward, not even requiring the AR/DR comparison; if one character has a clear advantage over the other, they get Edge. Easy. Wanting to gain Edge will inspire players to put themselves in tactically advantageous positions, if they know you're pretty open handed with it, and I kinda feel like that's the system working as intended. Granted, I tend to make it rain benefits, because one of the best bits of GMing advice I ever got was, "Don't be afraid to let your players be cool." Edge is definitely a means by which the players can pull off some cool shit.
Also, once the player get comfortable with their characters, they'll probably be pretty quick to point out when their qualities, or gear, or whatever generate Edge.
Now, maybe I'm wrong, and something about the system will actually be a big enough speed bump to slow down game flow; I haven't actually brought the beginner box to the table yet. Right now I'm optimistic, though.