Isn't McQuade Irish? So maybe it's proununciation is determined by how Irish sounding one kept the name when their ancestors came over? Plus, just because it's spelled with a Q here, doesn't mean it's pronounced with a Q sound.
Like the name Sinead, also Irish, is not pronounced the way it looks phonetically, pronounced: Shin-AID. There are plenty of Irish/Scotish names pronounced nothing like they are spelled.
There's singer Sade who pronounces it Shah-day.
I had a roommate in college. She kept talking about a family, pronouncing their name as "Cone," mostly because of her Jewish - Long Island accent. Turns out the name is spelled Cohan, which I would have pronounced like "Coe-Han," same as the singer, George M. Cohan, who created the Yankee Doodle Dandy song.
Also for the pronunciation of Q, I think the Canadians pronounce their city, Quebec as "Kay-bec," keeping the French pronunciation, whereas Americans pronounce it as "Kwa-bec."