I'm curious. Could a beanbag round from a beanbag shotgun (your typical Law Enforcement beanbag round) go through a vehicle's windshield?

No, the beanbag is not designed to go through a windshield. They have what is called a breaching round if they need to break glass. They would target the side windows and not the windshield. Side windows will shatter, the windshield will only crack.

No, but it could crack it.

A windshield is made from safety glass, which means it takes some major force to go through it. A baseball bat for instance won't go through it, even as it knocks the whole thing out in one broken chunk. Safety glass doesn't shatter.

It won't go through the front windshield but could go through the side windows.

soak it in water (make sure you keep the charge dry) and freeze it - it'll go right through