It did not deliver the 1948 address to the Association for Symbolic Logic at Columbus, Ohio, obviously. Weil read it for it, as we learn from Zorn's report about the meeting in the same issue of The Journal of Symbolic Logic linked in the OP:
"There were two invited hour addresses: N. Bourbaki, Foundations of mathematics for the working mathematician, and F. B. Fitch, Towards a demonstrably consistent mathematics. The first address was read by Andre Weil on Friday morning, Saunders MacLane presiding; the second was given on Friday afternoon, with A. A. Bennett as presiding officer."
That MacLane was a close Bourbaki associate (without formally joining) helped, and the consonance with the title of MacLane's famous book of 1971 is peculiar. But this was not the first or the last stunt Weil and co. performed on Bourbaki's behalf, see Barany, Impersonation and personification in mid-twentieth century mathematics:
"Because Bourbaki could not travel, write, or speak for himself, his personal manifestations relied upon impersonations. The self-styled “collaborators” of Bourbaki jointly prepared authoritative texts and joined with others to represent Bourbaki in a variety of contexts, often teasing or transgressing disciplinary norms as they did so. Relishing myth and misdirection, Bourbaki’s collaborators propounded his pseudonymous authorship as an open secret around which to establish or evade various forms of credit and responsibility in and beyond the mathematics profession."
Back in 1935 Weil engineered Bourbaki's first publication with a distinct flavor of a prank, complete with a made up country of origin:
"Under cover of cover letter, André Weil enlisted Élie Cartan, member of the Academy of Sciences and father of Bourbaki collaborator Henri Cartan, to communicate Bourbaki’s first mathematical publication to the Academy’s Comptes Rendus in 1935. According to Weil, Cartan was a witting accomplice, going so far as to consult with fellow academicians at a regular lunch group before endorsing the article Weil attributed to Bourbaki.
[...] Sending up the presumed familiarity shared within a scholarly community, Weil introduced Bourbaki in the cover letter with a knowing “Vous n’ignorez pas que. . .” – “You are not unaware,” or “As you know.” He situated the wayward professor at a café in the Paris suburb of Clichy, where he would fit stereotypically as a refugee from the vaguely Eastern-European invented country of Poldavia, recently “wiped off the map of Europe” by world events."
In 1937 Weil got some of the younger mathematicians at Princeton in on the ruse, including Smithies, Boas, and Tukey. Boas later gave Bourbaki’s textbooks the pride of place in Mathematical Reviews, where he was a contributor, but mentioned it was a pseudonym in some reviews. By that time, the group did not care much for hiding the fakery. Still, Boas and Tukey considered getting Bourbaki into American Men of Science in 1942.
Aside from the fake address, Bourbaki (Weil) "applied" to the AMS in 1948, and was rejected. But by 1949 Dieudonné took over as the chief prankster. Under his tutelage, Bourbaki "joined" the Société Mathématique de France and was eligible to join the AMS as well, under the 1946 reciprocity agreement. It took Kline, the AMS secretary, considerable ingenuity to find reasons to reject him again this time (biographical discrepancies between Weil's and Dieudonné's applications helped). The new application was handwritten no less, most likely, by Dieudonné himself:
"Dieudonné’s Bourbaki was born in Cucuteni, Moldavia, on 12 December 1886, elected to the Royal Academy of Poldavia in 1917 and the SMF in 1949, and presently employed at Dieudonné’s institute in Nancy. His 1910 doctorate came from Kharkov University, a real institution but sufficiently remote as to be unverifiable. Previous employers included the real Dorpat University, in Estonia, and the fictional Zorngahr College, an apparent portmanteau of German algebraist Max Zorn and Weil’s first employer in Aligarh.
[...] Most of the biographical claims were, in practice, unverifiable. Kline could neither write to far-off universities or possibly defunct academies, nor assert with incontestable authority that they did not exist – notwithstanding his justified certainty that the claims were invented. Bourbaki’s Rockefeller Fellowship, however, could be easily assayed from within Kline’s own professional network. He wrote to the foundation’s Warren Weaver on the pretense of checking Bourbaki’s fellowship history, but really as a chance to vent his frustration over the undignified behavior of the French upstarts. Even Bourbaki’s discrepant signatures earned a remark, having deteriorated from that “of a determined man” in the first application to a “cramped” and “infantile” one."
Hille, a recent AMS president, still advised Kline to join in on the joke and accept Bourbaki, and he might have been right. Bourbaki (Dieudonné) did not take the no lying down, and responded with "indignation" that by the reciprocity agreement "A.M.S. had no right to scrutinize" the application. As Hille predicted, "standing on our dignity will not get us anywhere and may expose us to ridicule".
"The AMS had to pretend to take the application as a sincere attempt to gain membership from an individual in order to challenge the premise that Bourbaki should be eligible. That is, they rejected the application because they knew it to be a farce, but their procedure for this rejection depended on an elaborate performance of believing the application to be genuine."