Yes, it is possible and very probable.  All the potion keeps have the same odds. The odds are split among the potions each level offers; lesser, greater, superior.  The odds vary by number of potions you win.  And, there is a constant 10% chance of a non-potion award across all levels, split between beer mugs, green shards, and ancient shards.

In stages 8 thru 11, the total odds of getting lesser shard(s) in any quantity of 1 to 5 are about 2/3.  You can get just one shard (20.5%) from those levels, in stage 12 the minimum goes up to 4.