No, says the Supreme Court (Baroness Hale dissenting), allowing the appeal and restoring the judgment of the ET in President of theMethodist Conference v Preston.
The minister carried out her functions under an agreement that entitled her to a stipend, accommodation and a pension; she paid tax under Schedule E, and was entitled to holiday and sick pay and subject to the possibility of disciplinary action. But the ET had felt bound by President of the Methodist Conference v Parfitt  ICR 176 to hold that the spiritual character of the arrangement meant that there was no intention to create legal relations, so no contract.
The EAT and the CA had disagreed, holding that held that the reasoning of the CA in Parfitt could not survive the majority speeches in a more recent HL case, Percy v Board of National Mission of the Church of Scotland  I.C.R. 134.
The majority of the Supreme Court holds that although there is no presumption against an intention to create legal relations in the appointment of a minister of religion, a consideration of the detailed internal arrangements of the Methodist Church leads to the conclusion that in this case there was no such intention; so no contract.
The gist of Baroness Hale’s succinct and pragmatic dissent: ‘it quacks like a duck and swims like a duck.’