An interesting experiment with the transferability of symbols and images. The photo of this plump pigeon doesn't resonate with what I think of when the Holy Spirit is described as a dove in the Gospels! The idea of this juggernaut flapping around the head of the Son of God has the incongruity of a Monty Python sketch that didn't make it past the director's cut! Urban pigeons are more evocative of lost sinners than the third member of the Holy Trinity.
Living in Aberdeenshire I might be more inclined to think of the Holy Spirit when I see swifts flying like feathered arrows with a mind of their own, or geese flying home in formation honking their conversation across the skies, or, when on the hills, the curlew's long drawn out cry of longing touches deep recesses of yearning I thought I'd forgotten.
Now and again, ornithology overlaps into orni-theology, as observation of birds occasionally coincides with more existential questions. When Jesus spoke of the birds being non-anxious, it's worth remembering his point of comparison was specifically anxiety about food and clothes and accumulation and the real grounds of security in the providence of God.
I'm not sure Jesus would use the urban pigeon, a stomach with legs and a beak, as a model for human flourishing now. As a metaphor for greed and over-consumption that chases others away from life's essentials,it forms the basis of a parable for our time. Only once have I seen a pigeon taken by a sparrow hawk - it was too heavy to get off the ground fast enough. Hmm.