Yes, the process seems to have been devised after a lot of wrangling, partly because the authorities didn't want to treat a gender reassignment as if it was the correction of an error (as had been done for transsexuals before the April Ashley court case) - hence the creation of the Gender Recognition Register. (According to trans friend, the certificates based on the GRR to begin with looked slightly different from a real certificate, thus blowing the gaff as it were. That got changed!)
I get my info from gov.uk and know nothing about genealogy, so would be interested to hear from family history buffs about this. For instance, gov.uk says a marker is put on the original registration linking to the GRR, but I'm unclear whether this is for the public's benefit or just for Registry employees.
In other words, could a clever genealogist find both girl Jane and boy John (all other parameters the same) and, if so, will the system that returned the search results tell him which is which as between the main register and the GRR?