I've been able to do some checking. The story found on Tulane's web site came originally from a book titled "Forty Years a Gambler on the Mississippi," by George Devol. It was repeated in Herbert Asbury's book "The French Quarter." Devol's account takes the company from its formation in October 1861 through the fall of the city in April 1862.

Several New Orleans newspapers carried stories or notices about the company. It met and elected officers on October 7, 1861. The Captain was Dr. William H. Berthelot, a native Georgian who graduated from the University of Louisiana and opened a practice in New Orleans. The company was named for Mr. J. M. Wilson of the city. The men furnished their own horses and equipments. A Dr. Elliott furnished a stable for the animals, and most company meetings and drills occurred there. There is conflicting information on the names of the other officers. One paper says they were 1st Lieutenant Thomas N. Boylan and 2nd Lieutenant J. M. French. Another says 1st Lieutenant George Moore and 2nd Lieutenant Thomas N. Boylan. By March 1, 1862, Moore had replaced Berthelot as Captain. There appear to have been 50-55 men in the company. It was associated at one time with the First Brigade, First Division, Louisiana Militia and later with the Second Brigade of that division. The last thing I found about them was dated March 1, 1862.

One account of the company's drill stated that they held it at "a fine spot on the lower end of Canal street." Afterwards, the men went to Galpin's Restaurant for a party that lasted more than an hour.

I'm not buying all of Devol's story. There certainly could have been gamblers in the company, but it seems unlikely that they all could have furnished their own horses and equipments.