I'm assuming the seeds would need to come in through the Gibraltar straight, which is not exactly wide... Also the Med is saltier than the Atlantic, not sure if that would be a problem for mangroves.
here's an article I found about dispersal of floating seeds. apparently there are some obstacles due to them sinking mumble mumble salinity:
https://insideclimatenews.org/news/19072022/mangrove-seeds-o...
Most mangrove propagules don’t travel far. They drop straight under their parent tree or get trapped in the tangled roots of the surrounding mangrove forest and take root a few feet or miles away. But long distance dispersal across oceans and seas is still important, said Van der Stocken. If mangroves need to expand their range because of unsuitable environmental conditions from climate change or weather events, as in Texas, being able to spread their genetic material long distances on ocean currents becomes important, he said.
Across the globe in the Atlantic and Eastern Pacific mangrove populations, including those along the Gulf of Mexico, reduced water density was less apparent in the study models. However, the model found these regions might develop saltier water than the Western Pacific. Even if propagules travel the same distance, increased salinity might affect their survival, which will have implications for the dispersal dynamics of mangroves in those regions.