I say yes!
And it need not be that way according to the General Instruction of the Ordinary Form of the Roman Missal, as muddled as that instruction for the Responsorial Psalm is! But this is typical of Ordinary Form instructions, alas!
Here on some highlights from the GIOTRM, #61, from The Structure of the Mass, Its Elements and Parts:
It is preferable for the Responsorial Psalm to be sung, at least as far as the people's response is concerned....normally the congregation sits and listens...taking part y means of the response, except when the Psalm is sung straight through, without a response. (My comment: Of course this is double talk which is typical of the Ordinary Form instructions, but happily it makes it clear that the Psalm can be sung straight through without the tedious refrain between verses! Why not simply sing the refrain at the beginning and the end and be done with it????)
...Instead of the Psalm assigned in the Lectionary, there may be sung either the Responsorial Gradual from the Graduale Romanum, or the Responsorial Psalm or the Alleluia Psalm from the Graduale Simplex... (My comment: This makes it abundantly clear, or does it?, that the Gradual can be substituted for the Responsorial Psalm in the post Vatican II Graduale Romanum or Graduale Simplex! How many people in the Church know this and have these resources been translated into English?????
So much for clarity, but who in the Most Blessed Name of God and all that is Holy even reads the GIOTRM? I don't know of many priests who have!)