No - it should not at all. Give it a gentle rock, just don't shake her up. The CO2 blanket and the positioned airlock will help you avoid oxidation.
That being said, I take it you think you have a stuck ferment? Have you waited a few weeks and tested with a hydrometer several times over the course of a few days to ensure that you have not hit your OG, or to confirm that fermentation is indeed stalled? If you answered "no" to either of these questions, leave it alone for a more than adequate period of time before attempting to rouse the yeast.