I would think this is a possibility. So far as I can see, it would have to be done under Section 137 (of the Local Government Act 1972) which allows a council to spend a certain amount of money on anything, subject to two considerations:
1. There is a limit per annum for the total section 137 expenditure, expressed in terms of an amount per elector. It was originally £5 per elector, but inflation linking has increased it so that the figure for the current year is £7.36 per elector. This must cover the total of all section 137 expenditures by the council.
2. The purpose of the expenditure must be, in the opinion of the council, in the interests of or will directly benefit the area or its inhabitants, or of part of it, or of some of them. The benefit should be commensurate with the expenditure.
Clearly the second item involves a judgement. So it is up to the council to judge whether money paid to support a youth worker attached to the parish church will give a commensurate benefit to people within the parish. There are no hard and fast rules, and the judgement would only be challenged if it appeared grossly unreasonable.
A technical consideration is that section 137 is regarded by some as not allowing payments to an individual person. In this case, the more likely practical implementation of the policy would be to make a payment to the Parochial Church Council to help pay the wages, which avoids a payment to an individual.
