I dont know about the challenge.
If you want to know whether saving in fiat or bitcoin, which will yield more profits at the end of 52 weeks,Bitcoin would yield you more profits.Even though bitcoin price is highly volatile,now in the current situation,Bitcoin is performing very well.We could see that on the first week of january, most of them predicted that bitcoin price would fall to $500 again, but it didnt happen. Instead bitcoin price recovered from $750 and now its almost around $1015.
Theres really a difference regarding on saving bitcoin compared to fiat and as you mentioned bitcoins price is volatile on which it has really the possibility that your savings would grow bigger because of moving prices of bitcoin which means its really worth it to save it on longer runs. 52week challenge is saving up for a whole year.