Can I ferment a biga in the fridge for 36 hours before baking a pugliese loaf?

Yes, you will still get a good result if you retard (refrigerate) your biga, although I recommend making a desired dough temperature calculation when you mix your final dough to get the bulk ferment off to a good start at about 76°F. You can adjust your water temperature to achieve this. A long, cold fermentation will possibly develop more flavor. Alternately, you can add less yeast to your preferment (biga/poolish) and add a portion of your overall dough salt (but don't forget you added it when doing the final mix!). This slows the fermentation down and would allow you to preferment at a higher temperature for the 12-24 hours. Another and possibly easiest option for you is to simply ferment the biga as the recipe states, but for a shorter length of time. Try 8 hours at 72°F. Happy baking!