Idk about 'profitable' it all depends on luck. Your luck retaining picks and your luck with drops. Nomal mode is definitly not profitable imo, hard mode is less not profitable due to elite tomes. Honestly, I don't really keep track of my cost of picks vs. cash made from drops. I don't sell my crap unids to improve my income, I id everything and salvage most junk drops if it salvages into mats I use for other things. I usually chest run in hopes of getting that rare item that makes it seem worth it. Most stuff I have/use on my characters was dropped to me, I have traded for some stuff but it's a small % of what I have.
http://archive.guildwarslegacy.com/15/15%20The%20…%20Run.003.html
There is some math on it in that thread... just change the 3 on the end to 4 thru 7 to see the rest.
Just today I broke 10 picks running chests for a few minutes but got 2 superior vigor runes, random luck is random like that (Halcyon Job, lux sin chests). Most times you probably won't make money but there is always a chance at a string of good luck.