Yes, but the delay is minor and deliberate.
There is a signal delay of around 200ms (roughly 6 frames at 30fps). This latency is a short buffer to allow the Switcher Studio app to synchronize video and audio as well as process the sources for optimal video output.
When monitoring audio using headphones, you may notice a lag behind the realtime audio. However, the audio will sync with the video output, which you can verify in the Live pane in the Switcher app interface.