Overall yes, but each startup is unique, and requires work and certain character traits and developing one cultivates talents, skills, connections, and business intelligence.
Each lottery ticket purchased is a no-skill crapshoot. People who are attracted to it tend to be looking for short cuts in life, not rolling up their sleeves for the hard and uncomfortable work of entrepreneurship. And unlike a startup, the lotto confers no personal benefits along the journey even when it fails.
The first part of your post is a great point. Building a startup, like studying hard in college, builds character/skills/talents/networks/knowledge that might be valuable to you in future endeavors.
These traits 1) help soften the downside of "losing" the "startup lottery" (making it non-analogous to the actual lottery in pure mathematical terms). And 2) perhaps also might help explain any measured difference in outcomes between startup founders and lottery winners.
But the "People who are attracted to it..." portion of your post doesn't seem necessarily true and is a pretty harsh/puritan attitude. Do you have any hard empirical data supporting these claims?
Defore testing this claim, and for your own sake, we should investigate parent's original question: do we see a similar pattern with startup "winners"? Because if so, your reasoning here might have disturbing entailments for the entrepreneurial set ;-)
Each lottery ticket purchased is a no-skill crapshoot. People who are attracted to it tend to be looking for short cuts in life, not rolling up their sleeves for the hard and uncomfortable work of entrepreneurship. And unlike a startup, the lotto confers no personal benefits along the journey even when it fails.