Your proposed plan is one that I've done a few times on remote vehicle trips . . . the phone is basically $x/day insurance against a serious problem. The best result is if you never get anything for your money.
In my case, I was able to find a local communications company in Portland that rented them for $10/day, so that's a little cheaper but I had to pick it up and drop it off. Don't know if you'd have a local option. The phone's easy enough to use, though it seems a bit bigger than you'd expect based on cell phones. (Of course, the whole concept is implausible magic, so who can complain?)
I would add that I find the sat phone to be a big improvement over the SPOT or EPIRB units. I don't know about climbing, but at least on a vehicle trip, there are a thousand potential problems that fit between "all's well" and "rescue me." Having two-way communications can really help. (The new Delorme InReach seems very promising for this reason.)
2007/2012 custom Jeep Rubicon expedition motorhome
2004 Jeep Grand Cherokee
2006 Honda PS250 Big Ruckus Expedition Scooter
1996/2002 Honda XR600R highly-modded