I doubt it especially if the older heir had married and had children. When Prince Albert married Victoria, he did not have to give up succession to the Saxe-Coburg duchy and eventually one of Albert and Victoria's sons inherited the duchy. Also British royals who married into foreign royal houses did not lose their succession rights. I know that the Norwegian royals are in the line of succession for the British throne, but now I am wondering if the same is true of the Swedish and Danish royals.
I think it was pretty unusual for Philip to give up his rights - Queen Anne was always called princess Anne of Denmark before she became queen, due to her marriage to prince George of Denmark. Her husband stayed the "prince of Denmark" through the reigns of Charles II. and his father-in-law James II/VII., but was naturalized by William III. and created Duke of Cumberland in 1689. While from then on, his wife used his ducal title, she still held and used the title "princess of Denmark" as well.