Not impossible but not wildly likely, because there is no evidence that Shakespeare took an interest in the doings of either Portugal or Spain. It is very, very obvious that Shakespeare STUDIOUSLY avoided politics and religious issues in his vast output.
He survived a change of monarch that way. He survived the Puritans' hate of theater that way. He was a survivor.
Spain was a huge issue for England, but Shakespeare doesn't mess with that issue. He does mock Italian courtlinesses, their exaggerated politeness which the English found hilariously affected. He does set a play in Verona, in Italy.
But that has nothing to do with Spain or Portugal or slavery.
Elizabeth I had a dislike for slavery but was told by her advisors that if she didn't engage in it, others would, and they would use it to get power over her and her country. She hated it, but her first duty was to keep England from becoming a Spanish province, which it almost did. If weather had not diverted the Spanish Armada, it might have.
Serfdom, which is the name given to Europeans enslaved each other, belonged to an earlier time. Sort of. In Shakespeare's time, you still couldn't be "masterless men." It was illegal. That is why Shakespeare's troupe needed the title of "the King's Men." This kept them on the right side of that law.
Shakespeare seems to know you can't sell tickets unless you give people characters they can love. He also knows you need the occasional truly nasty villain or people won't get excited enough, and they won't buy your vision either.