If you bought the logs and fletched them you would recieve profit and i think you only lose like 10gp per bow, so overall you'd be gaining money I guess
Even by fletching your own logs you still lose some money
Say you brought a maple log for 58 each, fletched into a maple longbow and alched for 192 each, this gives you 134gp profit however you have the price of nature runes to take of this, which are roughly 238 each.
This gives you a loss overall of 104 per alch, doesnt seem much on its own but it adds up quickly