Assuming you don’t recycle your paper plates and they go straight to land fill then using a ton of paper plates will remove at least a ton of CO2 from the atmosphere…
There is a kernel of truth in the statement, paper plates contain some carbon, so yes, they do remove a little carbon from the atmosphere.
However…
1) Paper plates are not made of CO2
2) The trees cut down to make the paper plates were absorbing CO2 when they were alive
3) Manufacturing and transporting paper plates burns fuel, which sends CO2 into the atmosphere