Yes, a dog can be trained to pee according to a time-table. The most important thing is not to let it pee where it's sleeping. Once that happens, it will take a lot of re-training to change its dirty habit.
Generally speaking, dogs do not pee where they sleep. Like little children, they are less able to control themselves when they are young. So you have to be more atttentive to their needs when they are puppies. Another thing to note is that dogs very often feel the need to go after a meal and after they had a nap. So when you train your puppy to pee on schedule, those are the best times to take it to wherever you have decided should be its toilet. After a while, the puppy will pee on cue when it's led to its toilet.
When the dog grows older, it can control itself better. Then just twice a day is fine. If it really needs to go in a hurry, it will always alert you, usually with low-pitched whining. Just remember not to let it get into the habit of wetting its bed.
Is it harmful or unnatural? I don't think so. We humans can learn to pee at certain times and we have not really suffered for the habit. I have had dogs that were trained to pee on time and they had all been very healthy. My friends who have many dogs also do not see any problem with this kind of training.
