ancuanatuath
According to three sources, yes:
1. NLS OS National Grid maps show both 109 and 4 here
2. Cadastral parcels show an outline of the house, which usually indicates a flat
3. There are 2 UPRNs for this building. For one of them the numbering continues consecutively along the odd numbered houses of King's Gate, and for the other the numbering continues consecutively along the even numbered houses of Moray Place

I've moved the address tags from the building to entrance nodes, positioned according to where the paths lead (changeset/132510554)