Yes, they would. The lottery is about giving up something of little value ($1 or $2) for some entertainment and the chance at a truly life-changing situation. I doubt anyone is unaware there's almost no chance they win, and that they're losing on every dollar they spend. Interestingly, the lottery is occasionally +EV to play.
I otherwise agree, people are bad at gambling, probabilities, and understanding the long term. I play poker, and poker players are constantly furious that their 80% favorite hand doesn't win 100% of the time. 80% feels like a lock.
Some people don't care. They want to gamble, and they have no regard for what they lose in the process. I think many humans are just wired this way, or perhaps it's cultural.