Diane Keaton is/was a very good singer. She sings in ANNIE HALL and RADIO DAYS, very well in both. Of course, she did stage musicals (HAIR) early in her career, so I know she can sing.
Yes, I think it might have been wise to either rethink the cast of the MAMMA MIA men (none is exactly a box-office draw, so they could have used stage actors who could sing like Tom Wopat, Brent Barrett, Marc Kudisch), or hire dubbers if they were set of three men to be the actors who were cast.