Not as far as I recall, at least not among the major nations. I can imagine some of the minnows may have missed players, as rugby was very low key in most countries other than the Foundation Eight. There were only 16 nations at the 1987 tournament (and South Africa wasn't there for either 87 or 91).
The other thing to consider is that, while the game "officially" went professional at the end of 1995, the reality was that the 1980s and early 1990's was the "Age of Shamateurism". Players were unofficially paid to play rugby, or set them selves up with "Promotional Companies" exploit a loophole in the IRFB Regulations that allowed them to indirectly earn themselves an income from the game.
By 1987, most rugby players in the Foundation Eight, at least at test level, were being paid to play by one means or another.
Just off topic a little (but related), if you are interested in the story behind how rugby became professional, get a copy of "The Rugby War" by Peter Fitzsimons (published by Harper Collins). Its a fascinating read, and tells the story of how rugby was very nearly hijacked by the World Rugby Corporation, a Kerry Packer backed organisation that tried to set up a professional "Rugby Circus" in 1995, something similar to his "World Series Cricket" that led to the 50 over "pajama" game. If they had succeeded, the international rugby scene would be vastly different from what it is now.