AFAIK @Joel Becker's introduction to EA was to find a good use for his earnings from his YouTube channel Messiseconds. 

Depends on the hobby and how good you are. Some things are relatively easy to monetize (you can teach lessons or do live performances), but even in those cases, you'll be competing with people who do your "hobby" as their job, and you're probably better off doing more of whatever your job is (working extra hours, freelancing...).

The thing I do is play games in tournaments, which is less common that streaming/gigging/etc., so this analysis may be of limited value, but: I've made something like $75,000 playing Magic: the Gathering and Storybook Brawl over the last four years (donating ~80% of that), but it took thousands of hours to do so, and a few unlucky turns of a card could have cost me most of the money. And I'm in the top 0.01% among people who try to play those games seriously in terms of success; many people roughly as good as me have put in more time to earn less.