In some cases, sadly, yes. Or being in management brings out the bully in them.
My ex manager was the first member of staff in my then very small company. He was automatically made manager of the two of us who joined subsequently.
I have always got on with him very well, but he essentially didn't have to manage me. I turned up, cracked on, and did well. However, he bullied the other guy shamelessly. He just had no strategies to handle the fact he didn't like him personally, or to address his poor performance.
Time passed, we grew, more staff joined. All of them put under his management - some he liked, some he didn't. You can imagine how it went with the ones he didn't. Whether he liked you or not, nobody liked how he treated the others. Yet in spite of the repeated infractions, he was continually promoted and conciliated.
He has ended up so conceited that it wasn't surprising at all that he began to turn his attitude upon his managers - who were even more cowed!
Meanwhile, I was promoted, carried out different roles. We were both offered promotion to the highest level. For whatever reason, he turned it down, and I am now his manager. For the first time in years, he turned his nasty attitude on me. It was the shock of his life when he got smacked down for it.