No you don’t need a Client ID created by the streamer as it’s not their application. To see if a streamer is live you use the Get Streams endpoint https://dev.twitch.tv/docs/api/reference/#get-streams with either the user_id param (which is their Twitch ID, a completely separate thing from Client IDs) or user_login param (their username).
The Client ID is what you’ll include in the request as the Client-ID header which will allow you access to the Twitch API.