[villagetinker]

OP, I have painted 4 rooms in our house, over the original builder flat off white paint, this was several years ago, and no problems. Here are some (I hope helpful) hints:
1. Use painters tape for all the areas with molding. Apply the tape and dry coat the edge, this will cause the painters tape to seal the edge. After the dry coat has dried 30 minutes or so, apply a regular coat of paint.
2. Be sure to get the correct knapp roller for the wall surface. This is very important.
3. Go over all areas with the roller at least 3 times in slightly different directions, ending in the same direction.
4. Before you move all the furniture back look over your work carefully, I am sure you will find areas where there will be little dots of the original color, we are still finding these several years after painting.
5. If your new paint is a wide color difference from the original, be prepared to apply a second coat. Allow the first coat to dry and carefully inspect the paint job. Most newer paints to a very good to excellent job at covering in one coat, but I had an experience of painting a light yellow over a medium blue, did not go well, actually took 4 coats to get a uniform coverage.

Finally, these textured walls are much harder (IMHO) to paint that a flat drywall, but on the good side they hide a lot of mistakes.

Hope this helps. good luck with your project.