Is it possible to use jam instead of sugar to make a dough?
Almost any substitution is about making a trade-off and understanding the ratios involved. In this case replacing 70g sugar and 50g of butter with 100g of jam and 200g of yogurt you both increase the moisture and remove the sugar crystals from the texture. During the creaming process (where sugars and fats are blended) the sugar crystals play a vital role in creating air pockets that will determine the final texture. 


  Why Do I Cream Butter, and What Happens If I Don't? 
  
  In pastry-speak, this process is described as "mechanical leavening":
  physically cramming air into a dough so that it'll puff up in the oven
  like a hot-air balloon. Google around, and that's what you'll be told,
  time and again. Creaming adds air. Air is fluffy. Fluffy is good. Good
  is great. Yay, cookies!


The yeast almost certainly made up for a lack of 'mechanical leaving' that didn't occur because of the jam, which lacked the crystalline structure granulated sugar would have provided. 

If one substitutes enough elements of a cookie recipe at what point does it stop being a cookie? Your own question answers itself that it is possible to replace A &amp; B with C &amp; D. It even looks like you created something quite good (I'm tempted to try it out), but is it still "a cookie" or something else all together? But then there is the whole "dipping it in milk" goal. This creation is more likely to breakdown in milk (as you have observed) and short of putting it between two graham crackers, probably always will be.