Definitely not for several reasons, first and foremost is the risk of introducing an infection, and secondly once beer is brewing you don't want to add any more oxygen/air to it as it can make it taste funny.
When you make it up it's a good idea to give it a very good stir not only to mix the ingredients but to oxygenate the wort and initially the yeast needs some to get going and establish itself.
The only exception to this is if it looks lie the fermentation may have stuck, then just a very gentle stir to try and rouse the yeast .