Well, you're joining the reserves shortly, presumably that shoudl have you qualfiied in your trade by the end of your first year of university. That'll give you three more years as an NCM working part time before you graduate. In that time you'll attend courses, goes on exercises, work on taskings... You will work in a number of different contexts.
After a couple years you'll start to feel a bit more comfortable in knowing what yu're doing, and you'll be promoted from gunner to bombardier. In that time you'll have seen a lot of different leadership approaches; some people will be good leaders, others bad. IT's easy to tell which is which; what's harder is to narrow down exactly *why*, and to take those as lessons for your own improvement. In thsoe first few years you will have your first opportunities to be a leader, and that is by leadership by example among your peers. Being fit, being knowledgable, being competent, having a good attitude, and being professional. You lead, first, by being a good follower, and then by being the type of soldiers your peers respect and want themselves to be seen as.
It's entirely possible that at that three or four year mark they may be looking to put you on your Primary Leadership Qualification where you'll begint o get taught how to teach, administer, and manage troops (all of them distinct from 'lead'; we do a poor job of teaching leadership, by and large we have a lot of excellent NCOs and officers who MENTOR leadership outside of the formal course structure). But getting PLQ would put you on the 'let's have this guy lead troops radar.
So you might or might not get some or all of your PLQ before component transfering to the regular force. A CT can take a surprisingly long time though.
If you come to the reg force as a competent junior Bombardier, with or without your PLQ course, and if you don't step on your own dick in the first bit, you'll before long start finding yorself in positions of responsibility simply by process of elimination. You will get more direct experience with leading others at that point. A reg force bombardier with six or seven years in will probably get leaned on quite frequently. That said, I don't see it as likely that a degree would get you promoted quicker.
As for carrying it over to the civilian world- that's gonna be a matter of how you articulat your experiences to a civilian amployer, and how you translate military leadership into more comfortable civilian terms. As that time approaches you'll be made aware of resources to assist with transition to civilian life.