Yes,the singers of Mamma Mia at the POW do sing live,their is also a live band/orchestra,sometimes seen sometimes hidden (don't know which for MM)
Why it sounds so good is because the singers are "miked",that is they wear radio mikes either in their costume ,or more usually for the ladies, in their hair.
Of course the reception from these mikes is amplified,which probably causes you to be amazed by the sound quality.
Sad to say it is only in opera houses now,or at concerts (like the Proms) that singers sing without electronic assistance.
Information courtesy of a great friend who is a stage manager on another musical in the West End.