I was recently doing some research into the history of the Old Georgetown Act and I came across a report of the very first project to be subject to review: 1504 33rd St.
The permit was applied for within weeks of the adoption of the Old Georgetown Act on September 22, 1950. The review was performed by the Commission of Fine Arts, which is the actual body that is authorized under the act to comment on permits. The Old Georgetown Board was created later in order to take primary responsibility for Georgetown (although the CFA retains the discretion to overrule the OGB).
The Post article sadly does not describe the proposal in detail, or whether it was approved:
The Georgetown Metropolitan 
The Old Georgetown Act established a three-member architectural advisory board (now known as the Old Georgetown Board) to review cases and advise the CFA. Project reviews began soon after the passage of the law, with the first submitted by the District government to CFA on October 11, 1950. The permit for alterations to the home of Mrs. and Mrs. George Potter at 1504 33rd Street NW became Old Georgetown Board case #1. The revisions requested seem to have been minor and the approved scheme was off-white painted bricks with black woodwork for the front façade. Approval was given on November 3.
…source https://web.archive.org/web/20190228224258/http://intowner.com/2017/03/14/georgetown-becomes-colonial-reborn-at-200-georgetowns-1951-bicentenary-celebration/