Теоретически здесь сказано что можно - http://www.mfa.gov.cy/mfa/Embassies/Embassy_Warsaw.nsf/DMLvisitin ... ment&print ...
Pursuant to EU regulations 265/2010 of 25.3.2010 and 562/2006 of 15.3.2006, aliens / third country nationals (except Turkish nationals or holders of other travel documents specified in relevant EU regulations) who hold a Long-Stay Visa (Type D) or valid Long-Term Residence Permit (Temporary or Permanent) issued by one of the EU / EEA Member States (except United Kingdom and Ireland) or Switzerland, may enter the Republic of Cyprus without a prior Visa, provided they fulfill the entry conditions in accordance with these Regulations. They may stay in Cyprus for up to 90 days in any six-month period.