Just wondering if anybody has ever done this. I would suppose the oligos could suffer, since they´ll be exposed to ionizing radiation for a brief period... but i´m not quite sure if enough to destroy them.
for being on the safe side please use 'x-ray safe film boxes or bags' (please 'google' for that by yourself). There are a lot of offers in the internet.
In addition you may wrap your sample(s) in lead foil.