Last year was our first time at WDW and we went straight to MK first, on a Sunday morning (this was September 18 I think). It was fabulous and it was very very quiet. Hardly anyone was there!
We arrived around 9.15am and were able to walk onto all of the following rides before 12pm:
Splash Mountain (twice)
BTMR
Haunted Mansion
Cinderella's Carousel (in fact there were only about 7 of us on it!)
Snow White's Scary Adventures
Pirates of the Caribbean
Jungle Cruise
and we spent a bit of time at the Frontierland shootin' arcade and even found time to sit on those big ole' rocking chairs near Liberty Square and people watch for a bit!
I know those tour guides are very helpful but from my own experience, it just wasn't that crowded Sunday morning. And we went during free dining as well but that didn't seem to affect the crowds too much on our trip.
So I say go for it!!! I plan on doing MK on a Sunday morning this time around too! Have a great time!