No, SOP (Same-Origin Policy) does not prevent what is traditionally considered CSRF (Cross-Site Request Forgery). In fact, traditional CSRF payloads exploit an inherent weakness in the SOP, but mostly the way browsers handle storage. For functionality to be vulnerable to CSRF, said functionality must be mutative and state changing, because the response cannot be read.
What you're describing would almost certainly be considered a new classification of vulnerability, in fact, it would be complete and utter breach of cross-origin access controls, not CSRF.
Furthermore, the necessary condition for a CSRF vulnerability to exist is the usage of cookie-based session management or in other edge cases some sort of automatically populated identifier, such as IP addresses. With or without, the SOP does not prevent this. The fundamental flaw that enables CSRF exits because of the browsers nature to programmatically populate requests with session cookies (in the most common case); this is agnostic of the SOP.
Simply put, by definition and inspection of the name itself, "Cross-Site Request Forgery", the entire concept is we're forging an HTTP request, we aren't expecting an HTTP response, which is what the SOP thwarts. This is why CSRF targets mutative functionality, which doesn't require an HTTP response to cause damage.
One could argue the SOP prevents the scenario you're describing, however, the scenario you're describing doesn't conform to the consensus criteria necessary of the CSRF vulnerability classification. Also, if you're inducing someone's client to make an HTTP request elsewhere, the response would be returned to the client, not the attacker, even if the SOP didn't prevent cross-origin reads, the response would be lost. Other forms of complex requests require preflighting.
SOP implementation predates the classification of what the consensus considers a CSRF vulnerability. SOP was not designed or intended to prevent CSRF attacks. The necessary inherent flaws that enable the exploitation of what is consider a CSRF attack are not mitigated by SOP.