Any automatic watch will run fast or slow depending on the position. Gravity does affect the components and so the watch will tend to run fast or slow depending on the position. You can verify this by placing your watch face-up overnight versus face-down. Many watches are adjusted to five, or 6, postitions to help even out this drift. A few high-end brands, Patek to name one, adjust to 8 positions. A worn watch is subject to continuous changing of position over the course of a day and so will tend to run a bit fast and slow depending on the level of activity, how much the watch is wound and even temperature. These factors can be taken into account when adjusting a watch.
It is possible to have the movement regulated so that the overall rate is brought into correct timing. Adjusting the movement is a more complicated process which can also be done, but you may get accceptable results from regulating it.
Hope this helps.