Is it possible to produce a tangible mass of DNA/RNA using a PCR reaction?
PCR amplifies only DNA not RNA.

A PCR reaction is typically within the  micro liter volume, and can go down to the nano liter volume for qPCR. The maximum volume of a PCR tube is 200 microliters. The maximum volume a 96 well thermocycler can handle per well is usually 100 microliters. So the maximum amount of reagent volume one thermocycler can handle at a time us 9.6ml 

I have never seen anybody scale a PCR to mili liter volume, as that would be rather expensive and excessive.

However if some some reason, somebody did do as you say, yes it is possible to obtain visible quantities of DNA. (Removal of impurities would be required first... ie unreacted dNTP, primers) And given that we can obtain visible quantities of DNA by extracting DNA from bacteria or salmon sperm.. I am sure a chemist somewhere would be able predict the physical properties of that DNA mass.