I don't know Connerys real reasons, and don't care.
Yes, it would've been nice to see him in the movie... I don't know were he could fit, but I have Darabonts script as an example of what could have been. And his scenes there were brief and far from spectacular, but they could have work good... not only a cameo.
Now, I agree that Henry's Sr. death reference was one of the top emotional moments of the movie. And that's not a good sign, because nothing new could compete with simple nostalgia... even in 'transcendetal' moments they used old music (marions theme, henry sr/grial theme) to get it to work.