I do really like the look of this car from what I've seen in photo's. I'm not convinced that Adler would have had a bigger influence on the design of the beetle though, the core of the beetle's design is a cheap utilitarian auto, thats what determined nearly every descision on the original car. The aircooled engine was lighter and had less parts, needed less power to drive it, the floorpan instead of a heavy chassis - etc etc. The original Kdf beetles were incredibly basic. The Adler looks to me to be a much more luxurious car for the time.
Having said that, it does appear that a few ideas were 'borrowed' from Tatra and incorporated into the beetle.
There is a thin link between Adler and VW, and that is Karmann - Karmann used to make the convertible Adler Trumpf:

And later went on to build the beetle cabrios.
Rob Amos
Happiness is a stock VW