How this works: Coachcomm is the system BYU has in place for a long time. It is a very good system and over 95% of FBS teams use Coachcomm system (there are about 4 headset varieties, at different price points). Historically, BYU was one of the few schools that did their own research on this product and utilized other depts to pay for the product (which lowered the cost per dept). Clever use of tech and keeping cost low. I recall well over a decade ago, BYU was actually teaching other universites (Bama, Clemson, Texas A&M, etc), how to make this more cost effective to the Universites. Where BYU excelled in this area was using same equipment but on international projects, so packaging product, making it much easier for deployment and setup was a no brainer. I believe (but this was a long time ago) that BYU used trunks to push product out to the fields, open the top and started plugging in devices (to side connections at field level). 

Prep for this is tested every game, from head sets to booth and phone to booth. Testing will occur (don't know if they still test like this or not now) 20 yards on one side to the other 20 yard line and 10 yards into the field. It is just a test to ensure as coaches do roam they are heard. Worse thing to do is not have your offensive or defensive plays not be heard on the field. 

Who calls the plays?: ARod sits in the booth and via the offensive channel or set on the Coachcomm headset will relay the call to the field. Each headset and battery pack has the coaches name on them. Coach Kalani head set can switch defense to offense, typically Mick Hill is the keeper of that headset and will give it back to the 2 lads managing the coachcomm system.  

Now to answer IF Arod calls the play, yes. It is relayed from booth to field. You are probably want to ask a different question, which might go like this: Once the play is called from the booth to the field, does Grimes change the play? Different question, might yield a different response. There have been times before that the offensive call is changed on the field. So, short answer. Arod calls the play but play could change on the field.

I know of only 2 ways to find out: Be on the offensive headset or talk to a coach that is on the offensive headset. 

Personally, I don't know what the big deal is about who calls plays or not. If the offense isn't producing enough TD's, then getting a different system, smoke signal or hand signals won't solve the issue. At that point, tech isn't the issue, it is more basic than that: Playing sound football fundamentals.