Based on the available documentation, no, it probably does not. Specifically, there is no indication that the App Check token is tied to a specific user, only to a specific app; another user of the same app could potentially pass App Check but cause the victim to send a request of the attacker's choosing within their own session, causing an attacker-chosen action to occur in the victim's account. This is what CSRF is.
With that said, it's unlikely to matter. CSRF is generally only relevant for apps where the client automatically sends tokens or credentials to the server with every request (or where the client is automatically trusted based on sheer ability to reach the server), and where outside apps can influence the client. In practice, that means specifically web apps, and only web apps that use cookies (or, in theory, HTTP authorization or client certificates) or where the authorization model is already dangerously open. Possibly there is a space in the overlap of reCAPTCHA Enterprise and App Check where CSRF is possible, but the primary use of App Check appears to be mobile apps, which are almost always going to fail one or both of the criteria above.