I think you should totally go for it if you get the chance. I cold emailed startups and wrote very personalised (albeit long winded) cover letters. If you objective is to learn, you really have to make that point shine through because there is no greater motivation in life than the desire to learn and people can see that. So don't get hung up with the low allowance (or none) and don't get discouraged by your friends riding high in their careers, do what you need to do to get that knowledge because (cue cheese) knowledge == power.