I think it depends on what level the title Finance Officer sit at for this particular school. As you can see from previous replies, it varies by school.
In my school, large secondary (2300 students), my job title is finance officer and not really stressful, it's mostly finance based admin. I do invoices, reconciliations, trips, pupil premium, payroll in conjunction with HR, parent queries etc. I did not have a finance background but have always enjoyed numbers.
Above me sits the finance manager who is a qualified or part qualified accountant, then above them sits the CFO. I'd say the finance manager role isn't too stressful apart from at audit time, they produce the monthly budget reports for departments, deal with pensions, HMRC submissions and VAT returns amongst other things. For their qualifications they would almost definitely get paid more out of education but for some the option of term time working and not too stressful works well if they have primary aged kids.
The CFO role is stressful and underpaid for the hours they do and the stress. They have overall responsibility for the budget and forward planning. Constantly trying to pluck money a non existent magic money tree. Lots of meetings with the head, SLT, governors, trustees, various committees, many of which are in the evenings. Trying to explain things to non finance people who just want 'the best for the students' whilst not totally grasping where funding comes from and the limits that it has.
If I was more qualified than I am, in my school I would happily do the finance manager role but wouldn't touch the CFO role with a bargepole.