With gas no absolutely. To preserve ice at room temperature using the pressure of a gas you should reach a pressure of one billion Pascals. Too dangerous for Penny safe...
In fact there are some imprecisions in the video Leonard cites two different methods to "preserve" snow flakes with an organic polymer. In fact these methods create a snow flakes replicas, they are called snow crystal fossils, because there is no more ice inside them. Both methods are describe here, have a look!
Leonard: "it will last forever I preserve it in a 1% solution of
polyvinyl acetal resin"
This is the Schaefer and Day technique  the solution Leonard is talking about is made from 1% of polyvinyl acetal resin in ethylene dichloride.
Leonard: "in fact is a pretty simple process, you see, Cyanoacrylate
are monomers which polymerize mmm... "
Cyanoacrylate are the main components of Super Glue this is easy method propose by the chemist Tryggvi Emilsson that you can do at home.
You have to choose one of these methods, you can't do both of them as Leonard (it seems) did... Take in account that Leonard is a physicist he doesn't know much about this stuff...;-)
 V. J. Schaefer and J. A. Day, Peterson Field Guides: Atmosphere (Houghton Mifflin, 1981).