Calibration Setup

I’m planning to purchase this kit (http://www.robotshop.com/en/reach-rtk-kit-multi-gnss-accurate-positioning-system.html), adn to integrate it in an outdoor rover/base station application.

Coming from the big ag space, where a lot of the systems from companies like Trimble can take up to several hours to calibrate and set up.

How quickly can a base station using reach be set up, and start sending accurate signals to a rover?

actually immediately;
you need to have precise gps coordinates of your base station which does influence the absolute accuracy of your rover; if you don’t know them reach can average the position in anything from 1 to 30 mins automatically; (you decide how long);
also you need a correction link: wifi or radio modem (like rfd868/rfd900 or 3DR modems) or 3G/LTE - depending on the distance you need;
if you also manage to do cable management away from electromagnetic interference (ESCs, motors, etc) you should be set up in a very short time!
(reading the docs will help save time too!!)

How accurate is the system typically if it is just placed on a tripod in a field and allowed to average in a minute or two?

From around the world to couple of cm (if you`r lucky)
Couple of minutes isnt enought for singel position in cm range. But usually around few meters
I say this because it is good habit to let gps collect some amount of data before averaging a position, just to rule out great errors