An important question is how much will he save over the course of a hike.
Alcohol is about 2 oz/ 1L water
Whitegas is 1.6 oz/ 1L water
Assume 1L water/day * 180 days (since he doesn't have any money, he'll cook all his ramen on this stove).
Total Alcohol = 360 oz = 2.8 gallons
Total Whitegas = 288 oz = 2.3 gallons
Total cost cost
Alcohol = $56 to $42 (HEET vs Bulk)
Gas = $9.2
Total savings = $47
Assuming you already own the whitegas stove + repair kit.
Assuming you can do the hike for $2200 (very hard), this is 2% of the cost. Not the best place to save money.
I think there are other places to save money that are more substantial, like 1 less night in town.