Will a dog remember its owner after a long period of time?

Yes, cats can remember their people, quite well in fact. I've lived with cats for most of my life and they're quite intelligent and deliberating animals.

As an example, I once babysat (catsat?) two cats for a friend who was on a trip out of the country. He was gone for two years almost exactly. When he returned, the cats recognized him instantly from across the room and literally ran to meet him as soon as he had stepped through the door. These cats were distrustful of strangers--even though they had warmed up to me, they still would not have done that even for me.

So the answer is a very definite "yes".