Hey Bud, I just received a copy of Aitken's book "Continuous Wave" and gathered a few more clues about the possible purpose of the tower that is shown in the picture.
Aitken says that Marconi pioneered the use of a vertical antenna to replace the horizontal antenna that was generally in use at the time.In 1900, the "raw" spark system was the only system in use. This was about 10 years before anyone knew how to generate a continuous (i.e.,sine) wave and even longer before anyone could modulate the signal with a voice. The Navy didn't get into the wireless business until the late 1900s and none of the original Navy stations were located on the Gulf Coast. However, the United Fruit Company was a heavy user of spark equipment and because Mobile is a port, I'm guessing that this was a Marconi spark station that was used by United Fruit Company (and perhaps others).
(The full citation:)
Hugh G.J. Aitken, The Continuous Wave: Technology and American Radio,
1900-1932 (1985), ISBN 0-691-08376-2.
According to the book, "In the Caribbean and Central America the
United Fruit Company, through its subsidiary, Tropical Radio, operated
an extensive network of land-based stations and relied on radio to
control the movement of its famous 'Great White Fleet'."
Tropical Fruit invented and patented the crystal detector and was
later merged into RCA.
Because Marconi sold its stations as complete packages of equipment
and coupled with the use of a vertical antenna, it seems likely that
this was a Marconi-supplied station.
Hollis W. Duncan