This is actually an interesting question. The
Department of the Interior's Office of Archeology and Historic Preservation (in its Historic American Buildings Survey) records (in 1972):
The bema, or
central reading desk, is surrounded by a balustrade with
turned and tapered balusters and a heavy, molded rail. A
trap door leading to an escape hatch and tunnel to Barney
Street is located in the floor of the bema.
Many note that it was common, even tradition for Spanish and Portuguese Jews to have trap doors and escape routes because of historical fears of the Inquisition.
However, Esther I. Schwartz, in a letter to the NYT editor (1983), states:
The origin of the tunnel story is unknown. During the 1958 renovation of the synagogue, despite extensive exploration there was no sign of an underground tunnel passageway, nor of an exit that would be required for such a tunnel. Furthermore, there is no mention of one in any of the early records.
The synagogue, built without a cellar, had a crawl space. It was common practice to provide a trapdoor for access. No one knows whether the present trapdoor is the original or was installed during the extensive renovation to the building in 1828.
Her qualifications are give there by Rabbi Theodore Lewis of the Touro Synagogue, who says:
Esther I. Schwartz, the author of the above letter, conducted extensive research on the synagogue during its restoration in the 1950's, unearthing original architectural plans from the library of Yale University and elsewhere, so in all probability she is factually correct.
However, what we tell our visitors today is that the Jews who settled in Newport did not live in fear but wanted to have the trapdoor serve as a symbol of the freedom of religion they enjoyed in America as contrasted with the persecution their forebears endured in Spain and Portugal during the Inquisition when the Jews were not allowed to worship publicly and very often worshiped in an underground tunnel in case the inquisitors would show up.
In a followup letter to the editor, Fordham University historian Elaine Forman Crane comments on the fact that the Jews who built Touro Synagogue may not have felt all that safe, considering that they were still not given full rights in Rhode Island.
Under these circumstances, it would not have been surprising if the Jewish people felt insecure. It is also not surprising that the plans for Touro Synagogue show no evidence of a tunnel. If, in fact, the Jewish congregation felt threatened enough to construct an escape route, they certainly would not advertise their intentions to the world.
Of interest to note, the Jewish Press (as well as many other places) records that
During the 19th century it served as a hiding site for runaway slaves who were escaping north via the Underground Railroad.
Though others claim that this is unfounded, and in any case, the Jewish community of Newport had mostly dispersed, and the Synagogue was not in use during the time of the Underground Railroad, though its cemetery was.
TL;DR:
There doesn't seem to be definitive answer to this, and neither historians nor Synagogue officials really know.