No, Jeff Dunham (born Jeffrey Dunham on April 18, 1962 in Dallas, Texas) has never appeared on the TV series America's Got Talent.
The man you are most likely thinking of is Terry Fator (born Terry Wayne Fator on June 10, 1965 in Dallas, Texas). He was the singing ventriloquist that won the America's Got Talent show in 2007 and credits Jeff Dunham as "a huge inspiration to me."
Both Fator and Dunham also have Christmas DVDs on the market, Fator's is Good Luck Charlie, It's Christmas! (2011), and Dunham's is Jeff Dunham's Very Special Christmas Special (2008).
Fator has an on-running show at the Mirage in Las Vegas, and Dunham is doing a North American tour through the spring of 2013.