Not deep... but do touch...

The less harmonica you hold in your hands, the more you can have in your mouth. The deeper you have the harmonica in your mouth (within reason of course), the bigger the tone. Once you have the correct depth in your mouth, your hands should touch your lips. This lip-hand, flesh-to-flesh connection, is part of your airtight cup for both amplified playing as well as acoustic techniques such as the Wa Wa (which both require an airtight cup).

Note that some players completely engulf the harp in their hands (me, Gary Smith, Andy Just, Etc.) and some allow the right-end of the harmonica to stick outside of their cup. See this month's videos submission from Aki Kumar (posting later in this month). The footage of Joe Filisko playing acoustic and of Aki playing with Andy Santana is a good example. Notice how Aki and Andy both do this when playing amplified (there's some nice side-profile views). The general rule of thumb is that the more distorted and bassy an amp is the more likely a player is to play like this... they don't have to work so hard with their cup to achieve this distortion, because the amp already has it. Something to think about...