Slave labor is a cute media label, same type of stuff as "assault weapon". As countries evolve, they get rid of more menial types of labor for higher technology industries. How many people in the US still make tennis shoes, shirts, and cheap plastic toys? We move up technologically. Countries moving out of 3rd world status start at these industries and go up from there, just like the US and Britian, and countless 1st world nations did. It's the natural evolution of nation-sized progress.
If by slave labor, you mean child labor and labor shops with long hours and few benefits (ie sweatshops), then yes, they are good for both economies. Actual slave labor isn't as widespread as the media would have you believe as most every country doesn't have an active slave labor trade today.
Every developing nation has used child labor and "sweatshop" type setups, including the US and Europe. 3rd world countries right now utilizing this type of labor is actually in the better. Now that people in 1st world countries can go home after their grueling 40 hour week, they have nothing better to do than complain about child labor and saving whales. What is the alternative domestic economy for these people?
Its subsistence farming, collecting garbage, looting, prostitution, and the like. Families will often sell their kids or worse if there are no places that accept child labor. Many end up in sex parlors and similar indentured servitude. Look what happened to Nepalese kids when we stopped buying their rugs because of evil child labor.
They get paid a higher wage through these shops installed by 1st world countries and large corporations than they do from the local economy. No one points a gun at their head and says "you work here or die". They do so on their own because the alternatives to making money are both less monetarily beneficial and more dangerous. With large factory labor paying a quarter a day, at least they get a roof over their head. You don't get that with prostitution or growing just enough dirt clods to feed yourself.
Tell me, what is more degrading, dangerous, and bad for the economy...people willing to work for less-than-US living standards, but greatly higher than their domestic living standard, or serving as child prostitutes to local dirtbags and rich people from 1st world nations that visit sex parlors overseas?