Yes, flying VFR through a MOA is perfectly legal...but not smart. While in a military aircraft I've been advised of VFR traffic numerous times and had to stop training to see and avoid the traffic. When in the middle of a 8 - 10k ft vertical maneuver with your T-38 wingman in extended trail where your airspeed goes from 450 KIAS to 200KIAS throughout the maneuver, you can't stop on a dime. I've had several near misses with GA traffic in MOAs including twice with the same Mooney that blasted through the heart of the Columbus AFB MOAs on different days. As Forest Gump said, Stupid is what Stupid Does.
Fly Safe! Don't Fly through a HOT MOA without talking to the controlling agency and understanding the activity in the MOA. Sometimes the military aircraft is droning at a set altitude block which you can easily avoid. Other times we are using the complete airspace with rapid vertical changes in simulated combat. That's why the controlling agency cannot provide flight following and advisories because they cannot predict the military aircraft's flight path.
Big Sky theory works most of the time but why risk your life and others.
Cheers,
George