Has anyone ever hosted Saturday Night Live and also been the musical guest the same night?

Yes, quite a few people have been host and musical guest of the same episode...

• Justin Bieber -- 9 February 2013
• Garth Brooks -- 28 February 1998
• Ray Charles -- 12 November 1977
• Miley Cyrus -- 5 October 2013 & 3 October 2015
• Drake -- 18 January 2014
• Lady Gaga -- 16 November 2013
• M. C. Hammer -- 7 December 1991
• Janet Jackson -- 10 April 2004
• Mick Jagger -- 19 May 2012
• Queen Latifah -- 9 October 2004
• Jennifer Lopez -- 11 February 2001 & 27 February 2010
• Ludacris -- 18 November 2006
• Bruno Mars -- 20 October 2012
• Willie Nelson -- 21 February 1987
• Olivia Newton-John -- 22 May 1982
• Dolly Parton -- 15 April 1989
• The Rolling Stones -- 7 October 1978
• Blake Shelton -- 24 January 2015
• Britney Spears -- 13 May 2000 & 2 February 2002
• Sting -- 19 January 1991
• Taylor Swift -- 7 November 2009
• Justin Timberlake -- 11 October 2003, 17 December 2006, & 9 March 2013
• Stevie Wonder -- 7 May 1983
• Frank Zappa -- 21 October 1978