Does Dunstan intend to follow Blazon’s advice?

Yes, Dunstan does follow up on his advice:

My visits to Mrs. Dempster weighed on me. She was not a troublesome patient at the hospital, but she became very dull; the occasional lightening of the spirit that had shown itself when she lived with Bertha Shanklin never came now. My weekly visits were the high spots of her life; she was always waiting for me on Saturday afternoon with her hat on. I knew what the hat meant; she hoped that this time I would take her away.