Yes, the key word in “Mass intention” is intention. Regardless of whether the priest spoke the Mass intention, it is his intention to celebrate the Mass for the intended person that counts.
Technically the wordings of the Eucharistic Prayers do not lend themselves to the regular recitation of the names of Mass intentions. The wordings lend themselves more towards funerals and particular anniversaries.
There is also the issue of concelebrated Masses, each priest is concelebrating the Mass with his own particular Mass intention, in such a situation it could be confusing for the main celebrant to announce his intention but not the other concelebrants.
No matter what the reasons for omitting it, a priest is not required to speak a Mass intention during the Eucharistic Prayer. He is only required to have the proper intention when celebrating the Mass.
