Using current technology, we would most likely render the earth uninhabitable due to the carbon emissions required to get it there.

If we had fusion & a space elevator it might be survivable.

We can borrow the reasoning from: https://what-if.xkcd.com/7/

That thought exercise involves moving 455 megatons of human off-planet. Getting rid of all plastic waste would in some ways be harder than that. Because we'd need to move that mass every year.

Current plastic production is about 380 megatons per year.