Without seeing the Last Supper image, I can't say whether or not it should be venerated. The Romanov poster? Definitely not. It is a lovely souvenir and commemorative item, but it is not an icon, even though the poster features people who are now proclaimed saints.
Was this image painted with prayer and fasting? No.
Is there a Church feast day dedicated to the tercentenary of the dynasty? No.
Is this image glorifying God, or the Imperial Family? No, yes.