It’s possible, but can be difficult especially if your natural texture is 2 or more patterns of curliness/kinkiness from your relaxed hair. For example, if your relaxed hair is like a 2a 2b in curliness and your natural hair is a 3a 3b your transition to natural hair with good care will more likely be a success, with minimal breakage at the line of demarcation.
However, if your relaxed texture is a 2a 2b and your natural hair is a 4a 4b, you will probably experience more tangles and more breakage at the line of demarcation. You will probably also feel like your natural hair is difficult, and hard to manage, but this is only because the extreme texture differences are at battle. Both requiring different needs in moisture, protein, and maintenance.
When I grew out my relaxer and transitioned to natural. I would say my relaxed hair ranged from 1b -2b, my natural hair has a varying array of 4b. Not to mention that my natural hair is fine, but my relaxed hair was even finer. Needless to say, even with the utmost care, I could only transition for so long before I had to let the relaxed ends go. Once I did, my natural hair was easy to manage.
But just to throw a wrench in my own theory. If you have thick, coarse strands and your natural hair is pretty healthy free from odd breakage and such. Even with 2 or more patterns of texture difference you can keep both textures for a while without a lot of breakage at the line of demarcation. However, detangle may still be a struggle on wash days.