That is down to how good the head teacher is and they can leave a good school.
Yes, definitely.
When I was at secondary school, we had an amazing head teacher - he was charismatic (he drove a shiny black Jag that he parked right outside the school), he was encouraging and motivating, and he got involved with school activities (for example, he and several other teachers were in the choir (male and female) and concerts were sold out). We were one of the top schools in the county, well-respected, a Centre of Excellence for Science and in 1998, our GCSE results were ranked in the top 10 of comprehensive schools in the UK.
Sadly, about 2 years after I left the school (just after my brother started there), he retired and a new head teacher took over. This head teacher had no presence, he didn't get involved with activities and the overall morale of the school dropped (for example, the choir dwindled down to a few year 10 and 11 girls and no teachers, and they barely sold any tickets to concerts). By 2013, the GCSE results had fallen, pupil behaviour was terrible, the Ofsted report had gone from Good to 'Needs Improvement' and it is now ranked one of the worst schools in the county (it's also now an academy).
Back when I was there (1994-2001), I would have sent my own kids to that school in an instant. Now, I wouldn't go near it. It's so sad, because it was originally a Grammar School, established in 1606, and as far as I know, it always had a great reputation
.