Depends on your range of motion currently, and level (if any) of discomfort.
I've got the 20yr perspective here - for probably my first 10 yrs or so of practice, I didn't have the best posture and didn't have a workout routine in place that did a bunch of core stretching and some core strength exercises - I was an all cardio (run, cycle, walk, hike, etc) exerciser
Then, when I did start to have some lower back soreness and stiffness on a fairly frequent basis at the end of my work days, I talked to a physical therapist friend of mine, who put me on an exercise routine that in addition to the cardio that I enjoy, now has regular (3 to 4 times a week) sessions of core stretching and resistance training exercises focusing on my lower back, neck and core, and frankly, in my mid 40's, with 20 years of practice wear and tear on my lower, lower back soreness at the end of a work day is a rare event now, but yes it still does happen occasionally, but far less than it did 10 yrs ago for me.
Additionally, I am now quite aware of my own posture when sitting in my doc's chair working on my patients, and most certainly nowadays move my patient chair into positions that make it easier, and less taxing on my back/neck. than I used to.
If you're fairly functional and comfortable with your back now, then with a solid commitment to a physical fitness routine to help develop and maintain the muscles that you use while working, you'll likely be able to practice. If you have a decent amount of discomfort already, even with PT work to help with those areas, then you'll likely be looking at issues in this profession....