A convergent boundary means they are pushing towards each other (not side by side nor away). That causes pressure that will most likely cause earthquakes until it settles down in position.
The earthquakes might be felt by the human population or not, depending on the strength of the movements involved and where they occur, but they will be registered by the seismographs around the world for sure. Every day, thousands of earthquakes happen all over the planet, and only a handful of them are felt by humans.
