Is it possible to earn Mega-Tickets without spending real money?

You can either buy them with Mega Bucks OR Gold bars ;)

According to Wikia it isn't obtainable through gameplay, and I never encountered it anywhere, so I guess they are right.

Gold is the real-money currency in AdVenture Capitalist, and cannot be obtained through gameplay.

Yes, you can earn Gold Bars through the gameplay, especially when playing the event games (such as Insert Coins to Continue). The gold is awarded when you reach certain number of upgrades. Gold also can be earned by Daily Deals, Daily Rewards and Spin wheel. In this way I've managed to collect over 240 through the gameplay within few days in order to buy Greet Suit (I was lucky enough to win 100 of gold bars in spin wheel).