If we were talking about traditional surrogacy, then the answer would be yes. In traditional surrogacy, as explained above, the surrogate gets pregnant by means of Intrauterine Insemination (IUI), and therefore fertilization occurs as it would through sexual intercourse: inside her reproductive tract.
However, traditional surrogacy is not used anymore nowadays due to the number of legal and emotional complications associated. So, technically, a more precise answer to this question—as long as we're talking about gestational surrogacy—is no, she doesn't.
Suggested for you: What Is IVF Surrogacy? – Process, Success Rates & Cost.