Question: the gametophyte for seed plants is completely independent of the sporophyte stage

Answer: Yes, A sporophyte (/spɔːroʊˌfaɪt/) is the diploid multicellular stage in the life cycle of a plant or alga. It develops from the zygote produced when a haploid egg cell is fertilized by a haploid sperm and each sporophyte cell therefore has a double set of chromosomes, one set from each parent. All land plants, and most multicellular algae, have life cycles in which a multicellular diploid sporophyte phase alternates with a multicellular haploid gametophyte phase. In the seed plants, the gymnosperms and flowering plants (angiosperms), the sporophyte phase is more prominent than the gametophyte, and is the familiar green plant with its roots, stem, leaves and cones or flowers. In flowering plants the gametophytes are very reduced in size, and are represented by the pollen and the embryo sac.