Dear Vincent,

Absolutely, yes, the priest may sing the entire Mass, including the words of consecration.  Well almost the entire Mass anyway, I suppose it wouldn't make much sense for him to sing the homily, as well as some other inaudible prayers.   But even the readings can be chanted!

Anyway, in the GIRM we read "In the rubrics and in the norms that follow, the words "say" (dicere) or "proclaim" (proferre) are to be understood of both singing and speaking"  (n.38)

Regarding specifically the Eucharistic Prayer and other presidential prayers, there MUST NOT BE MUSICAL ACCOMPANIMENT when the priest sings.  (n.32)  I know that it's a common practice for the priest to sing, for example, the Mass of Creation which has a song written for the Eucharistic prayer.  If the priest wishes to use this song, he must do so WITHOUT the organ  or other instruments.

In my personal opinion, it just sounds bad for the priest to sing a song without the organ, so instead he is far better off CHANTING the prayers, even in English chant sounds good without the accompaniment of other instruments.

Mr. Slavek