What would happen if I dehydrated fresh sausages for a couple hours?
You would potentially grow bacteria that would make you sick.  The production of cured sausage has to follow a specific process that makes use of the correct balance of salt, water activity, and acidity (often, along with the addition of nitrates) to create a safe product.  You can certainly make fresh sausage and cook fully, or refrigerate for a few days, or freeze for a much longer time.  Alternately, you can make beef jerky, and fully dehydrate thin slices of meat. However, I would not recommend playing with the age-old, tried and true, processes that have been proven effective for properly producing cured sausages.  

Given your edits, and your focus on fresh sausage, dehydration has no advantage, and as @rumtscho clarifies, poses a safety risk.  Either cook fully right away, or chill below 40F (4.5C) immediately.  When I make fresh sausage, I vacuum seal in bags and freeze what I am not using immediately.  This preserves the quality for several months.