It depends. If it is a situation where a school goes into special measures, the head leaves, a temporary one is appointed for a year, then a permanent replacement (or similar type of scenario) is found then no. The school I attended as a child has been through 8 heads in the last 12 years, it is as a result of deep issues in the school and LA (and it is in a mc area with decent exam results). That scenario then yes you should worry. However the teachers in my old school continue to work hard to provide a good standard of education, despite all the backroom politics.
Some years ago I worked briefly in a school that had been through several heads (acting and permanent) in a few years. There were deep seated problems within the school and it was a nightmare to work in. From the outside it looked a lovely, caring school in a leafy area. I don't want to say too much about what was wrong but I got out at the first opportunity and the staff turnover was huge.
So yes, I would worry, although obviously there may be a far more innocent explanation in this case. But I would want to know more. being a teaching head is very hard, but it's rare to have NO management time. I would want to know why - have they terrible financial problems, or problems recruiting staff?
I don't see how anyone can teach full time, and be a Headteacher.
At dd's school, the head teaches 2 days a week.
As I see it, small schools with teaching or part teaching heads tend to attract either first time heads, who stay for 2 -3 years and then move on to larger schools/non teaching Head roles, or they attract teachers at the end of their careers, looking for a step down from a large school, before retirement. Neither of these options is particularly good in my opinion.
It is a major concern for me too as dd's school are about to have their third head teacher in 4 years due to some fairly rubbish decisions by the governing body.