What happens if you try to drive a fishing boat along a beach  , with the propellers barely touching the sand?

If it's your own boat - it might do no real damage (other than to the paint on the prop) but you'd risk hitting a rock or something else in the sand that's big enough to damage the prop.  If the boat's a rental - you could get charged for a new prop because the paint will almost certainly be sanded off the prop from running it in sand and whoever rented it to you might just assume you damaged the prop.    

And you would want to do this WHY

You'll get sand/dirt in the cooling intake and destroy the impeller.

Pretty sure you legally have to stay a certain distance from the shore if you're going to drive a boat around, mostly because of swimmers and things like that. It's a safety thing and you could lose your licence if caught. Otherwise, you also run the risk of hitting rocks or other things under the water and completely destroying the underside of your boat and your motor which will cost you a ton of money.