Could Hank have been on steroids ?
Starting in the 1950s? Highly unlikely. Steroids didn't even become a big enough problem to get banned by the IOC until the late '60s, and that was because of sports like weightlifting. There's never been an account of steroid use in baseball before the 1970s.
Look, the steroids debate is a bit silly with respect to guys like Aaron, even independent of the timeline. The purpose of anabolic steroids is to build muscle mass. They don't suddenly give whatever muscle you have some superhuman strength that it didn't possess before. A 5'11" 200 pound dude who got that size naturally versus a dude who got there on roids will be equivalently strong (assuming one dude isn't fatter than the other).
While there were some smaller guys who used roids to get big enough to hit for any power at all (Brian Roberts, for example), the bulk of dudes who were hitting homers while on steroids are guys who had the classic roided-out look: Bonds, McGwire, Sosa, Palmeiro, even lesser lights like Brad Fullmer and Jay Gibbons. These are guys for whom the reasons for hitting dingers were obvious - they just got huge. They don't have the same look that a lot of the guys who hit lots of homers despite being smaller have in their swings: disproportionately large forearms, pretty lean through the middle, lots of wrist and really quick hips in the swings. Dozier is pretty much all of that, Aaron is almost the archetype of all of them.