No that is not where the word comes from. Slav is an English-ization of “slowanie” (what slavs call their group) which means “people of the word “ or people who can talk or something along those lines.
Yeah. In Polish Slav means a speaker, or person of our word. In Latin, it meant person who we can take to do work for free, but the Polish came up with the term first.
Our old word for foreigner is the same as non speaker or mute, Niemcy, which now specifically refers to the Germans. I guess they were our first foreigners.
https://en.m.wiktionary.org/wiki/slave