Is it possible to have braces if I have a jacket/crowned teeth in front?

Yes, it is definitely possible to have braces even if you have crowns on your front 4 teeth. Your Orthodontist will use special bonding techniques to attach the braces to the crowns as they are most likely made of porcelain (which is different than your natural tooth structure). You should address the issue now to figure out why the gaps are forming and prevent them from getting any bigger.