I think it's a very reasonable plan. That's exactly what I did when I was recovering from a fractured pelvis. Before I even looked a road bike again, I first put slicks on my hardtail MTB and rode her on the trainer. Then I took her out out on the road for awhile. Finally I graduated to my road bike, but since it's a Bike Friday with 1.3" tires, and steel, it's not too extreme or harsh. Riding the mountain bike, I didn't aim for speed, just to try to regain some fitness and get over some of my fears of getting back in the saddle in a semi-relaxed way.

Good luck!