The Poloniex customers from Russia claim that this problem is serious. They indeed now have to withdraw their funds as they begin to receive the emails:
Poloniex emails Russian users
How this will affect the financial position of the exchange (as Russian miners and traders are quite active) and its reputation, remains to be seen.
Notably, not only Russia will be affected, but also other embargoed countries among which are also Crimea (region of Ukraine), North Korea and others.