It's not entirely clear. FAR 5.102(a)(1) states that unless one of the exceptions at FAR 5.102(a)(5) exists (sole source is not one of the exceptions), the solicitation should be posted. A primary purpose for doing so would be for small businesses to learn specifics about potential subcontracting/supplier opportunities with the sole source prime contractor. On the other hand, 5.102(e) states "Provide copies of a solicitation issued under other than full and open competition to firms requesting copies..." which implies the solicitation had not been posted to the GPE. There was also a court decision (DIGITALIS EDUCATION SOLUTIONS v. U.S.) which ruled that for a sole source acquisition, the synopsis is analogous to an RFP.

Considering the foregoing information, the contracting officer may want to use his/her business judgement to determine whether to post the solicitation.