You wouldn't want to carbon date the average CDV, due to the margin of error and that a piece has to be removed for testing. However, an advertised old paper baseball item was carbon dated at the University of Arizona to definitively prove that it was modern for a court case. Though Man Ray forgeries were discovered by another test on the paper.
If you want to learn how carbon dating and other such highly advanced processes work, I recommend the following book (I'm the author
). Spectroscopy-- a non-destructive test that identifies the chemical makeup and levels at the molecular level using a handheld device-- would potentially be very useful for baseball memorabilia, photos to cards to uniforms. Spectronomuy is used to date many things including painting. Spectroscopy is something I see in the future of baseball memorabilia and is even used to determine if aging signs (rust, foxing, etc) is authentic. The devices are expensive, but everything's free after that.
The book also goes into all the issues in authentication-- margins of error in testing, limits of science, etc.
Link