No, normally there aren't any descriptions of audio cues and sound effects in subtitles. Closed captions feature not just dialogue but also descriptions of sound effects and other auditory cues for viewers who are deaf or hard of hearing, whereas subtitles are solely intended to give translations of spoken dialogue.
However, some video content might have subtitles for narratively important aural cues or sound effects, like music lyrics or on-screen text. However, closed captions offer a more thorough description of all the audio components in a video while subtitles often solely translate spoken dialogue.