No. Since the 2018 alignment of Slovak law with the EU Trademark Directive, the ÚPV SR examines applications only on absolute grounds, matters concerning the mark itself, such as distinctiveness and descriptiveness.
Relative grounds, meaning conflicts with earlier registered or pending trademarks, are not assessed by the office of its own motion. Instead, the owners of earlier marks are responsible for monitoring new applications and filing an opposition during the three-month window after publication if they wish to challenge a conflicting mark.
This makes trademark monitoring important for Slovak rights holders, since the office will not block a confusingly similar later application for you. Set up trademark monitoring with Trama to catch conflicting filings while there is still time to oppose.