Through the 2009 season, no. The Bobcats have played in four bowl games (1962 Sun Bowl, 1968 Tangerine Bowl, 2007 GMAC Bowl, 2009 Little Caesars Bowl) and lost each one.
Alabama
Auburn
Miami
Wyoming
January 1, 1962: Texas 12, Mississippi 7
the Alabama crimson tide won against the Arkansas razorbacks
Baylor Bears
Texas Mines
Nebraska won against Miss ST
Minnesota over UCLA 28-3
New Mexico State