Do you think different sources of carbs (sugars) would affect the rate of fermentation in yeast? Why or why not?

Yeast is a fungus and needs a supply of energy for its living and growth. Sugar supplies this energy (your body also gets much of its energy from sugar and other carbohydrates).
Yeast can use oxygen to release the energy from sugar (like you can) in the process called "respiration". So, the more sugar there is, the more active the yeast will be and the faster its growth (up to a certain point - even yeast cannot grow in very strong sugar - such as honey).
However, if oxygen is short (like in the middle of a ball of dough), then yeast can still release energy from sugar, but in these conditions, its byproducts are alcohol and carbon dioxide. It is this carbon dioxide gas which makes the bubbles in dough (and therefore in bread), causing the dough to rise.
Alcohol is a poison (for yeast as well as for people) and so the yeast is not able to grow when the alcohol content gets too high. This is why wine is never more than about 12% alcohol.