I asked about him on the Civil War Talk forum and had two replies.
Border Ruffian said that there was a IIRCC Connelly who deserted from the US Army and then enlisted in the USMC and won a Medal of Honor. His family later petitioned the HQMC for a name change.
M E Wolf had the accounts of the attack from the ORN and both definitely put our man at the palisades during the January 15th Naval Column attack on Fort Fisher.
I'll have to look into the IIRCC Connolly story and thanks E M Wolf.
Interesting Story. --Old B-R'er