Most people exploring Morocco overland are in Morocco proper, where there isn't the same strict control of foreigners as in Western Sahara. The checkpoints start at Guelmim and are spaced about every 100 km apart. One has to present one's ID or a printed page known as a fiche with these details (a web search for Western Sahara + fiche will probably give plenty of travel blogs with details on the police scrutiny). Plainclothes police are also present at the major intersections to report on what direction a foreign-owned vehicle takes.
Although Morocco proper has some sand dunes in the east which are popular with tourists, these are not the "real Sahara", which is traditionally considered to start at Guelmim.
Yeah, there is a great difference between morocco and occupied western sahara.
My morocco experience started in western sahara - and it was interesting to watch, but no fun, to be bothered by secret police all the time. I had intentions of traveling around there and meeting local population and getting into the sahara, but this was not really possible in a way I wanted. I played the naive tourist quite well, so I was not too much pestered, as being a european tourist, because the king himself has ordered to all police to be nice to tourists. But they really do not want journalist, I had to convince many slimy assholes where I felt dirty to shake hands with them, that I was not a journalist, nver were and no intentions of becoming one. And since I really was not a journalist I decided to be it not worth it. But I have friends who drove around with a bycicle there and camping overnight, so that is possible, but not peaceful. And dangerous if you come too close to the border.
Morocco then again was really different, full of hippies and other tourists. It surely has dangerous spots as well, but I felt quite safe hitchhiking there and I even met young women, who did hitchhiking there, without being kidnapped or raped, but that can happen.
And the real dessert experience, well, I was south-east of Zagora, wich was quite touristic - but to me it seemed the "real Sahara" did also start there. I met local beduins who felt that way too, but yeah. The border to algeria was too close and too guarded. And in the real dessert there are no nation borders, who pester the nomad.
Although Morocco proper has some sand dunes in the east which are popular with tourists, these are not the "real Sahara", which is traditionally considered to start at Guelmim.