I suggest you do more reading on the Recruiting website in regards to what positions people with your types of degrees (still to be achieved I take from your post) can do. There are occupations that are some sort of engineer in the Army, Air Force, and Navy.
I don't know if you know the difference, but a Combat Engineer is a non-commissioned member, whereas the Engineer Officer is a commissioned officer who leads Combat Engineers. I always thought that the Engineer Officers were also called Combat Engineers, but I learned something today (even after 16 plus years in, who would have thought? lol ). Maybe some Engineer Officers or Combat Engineers can pipe in to give you more details.
http://www.forces.ca/en/jobexplorer/browsejobs-70
"Get some action?" If you mean deployments, then yes, a Combat Engineer (as do all the other engineering occupations) does have these opportunities, but I sincerely hope that you do NOT want to join the military just to "kill or shoot people". If so, then DO NOT apply to the military. The military is not a video game.
Training opportunities abound for all engineering occupations. Again, do some research on the Recruiting website.
"Switching" as you put it is called Occupational Transfer, either Voluntary (VOT) or Compulsory (COT). If it is your choice, then it is VOT. These are not as easy as you think or as easy as the Recruiting Centre will make it out to be. My strong advice is to do a lot more research and determine exactly what you want to do if you join the military. It is MUCH easier to enter into the CF in exactly what you want to do right at the beginning vice doing a VOT or COT.
If you haven't done your undergrad (Bachelor's yet), you might reconsider doing the Master's degree right away after 4 years of "fun" to get your undergrad. If not, all the power to you. As well, if you really want to join the military AFTER university, why don't you do your education in the military and not personally pay a dime towards it, i.e. RMC offers Civil Engineering? Again, do some research on the Recruiting website or visit one. They'll give you all the info you need, with up to date regulations/procedures.
As for the Master's, that is a different story for another day (you have to apply for it once in the military in order to get the mil to pay for it).