I boxed for 5 years - the last two professionally. When I boxed - in the projects - it was at a "real" gym.
I have also instructed people in classes and "boxing gyms". And I put that in quotes because I was more personal trainer that used boxing techniques and workouts for my clients. Probably in the same category you are in - you aren't looking at becoming a boxer.
You may be working with a great personal trainer but no well respected boxing coach is taking on clients that don't spar.
What you get out of your boxing workouts depends on what equipment and exercises that you do. If you gave me an example schedule I could probably tell you what to expect.
If you are "boxing" with a good trainer 4 days a week your work would include small amount of weight work (normal day might include 4 sets of 20 squats at moderate weight), it would include abdominal work every day, it would include speed work (sprints, jump drills, lateral movement), it would include endurance training (jumping rope, long jogs, shadow boxing), and it would include lots of heavy bag work.
What can you expect out of a real boxing regime? Answer is simple - an efficient body. A true boxing workout slims down your body to its optimal weight while retaining as much speed and explosion as possible. Don't be fooled by Rocky - that body doesn't exist at most gyms. Having large muscles is slow, lessens your length, and makes you jump to a higher weight class...
What do you need to worry about? If you aren't sparring then nothing will ever hit your head (my trainer did used to smack the sh!t out of me with his mitts if I dropped my hands). I would say for the new boxer the elbows would be my main concern - over extending is the #1 injury from experience. Make sure your hands are properly wrapped, you have gloves on when you are hitting something, and you work into the routine slowly the first few weeks.
The benefits of a good boxing routine. You will use muscles that you will never have a chance to use in your life. You will become quicker and leaner. You will get the best natural high you can get. And how do you know if you have a good trainer... he should be more worried about your intensity not your "form" or giving you "boxing lessons". If you aren't putting in the effort and just jumping rope and hitting a bag, you will see little to no results (other than sweating).