You can follow along, and I often do during the Eucharistic prayer, but I don’t recite it out loud. This goes along with the question of holding hands during the Lord’s Prayer or raising one’s hands, etc. The rubrics of the Church specifically reserve certain gestures and prayers to the priest. When the priest is saying a prayer aloud like the Eucharistic Prayer, you don’t say it also. Likewise, when the priest is praying and holding his up, you are not to do likewise. The orans posture, which the priest uses when he stands and prays with arms outstretched, is reserved for the priest. Is it expressly forbidden? No.
From Jimmy Akin:
Standing means standing without doing anything fancy with your arms. It is distinct, for example, from the orans posture, which the priest uses when he stands and prays with arms outstretched. It is also distinct from the hand-holding posture.
The latter is not expressly forbidden in liturgical law because it is one of those “Please don’t eat the daisies” situations. The legislator (the pope) did not envision that anybody would try to alter the standing posture in this way. As a result, the practice is not expressly forbidden, the same way that standing on one foot and hopping up and down as an effort to get closer to God in heaven is not expressly forbidden.
In general what liturgical documents do is to say what people should be doing and not focus on what they should not be doing (though there are exceptions). To prevent “Please don’t eat the daisies” situations, what the law does is prohibit things that aren’t mentioned in the liturgical books. Here’s the basic rule:
Can. 846 §1. In celebrating the sacraments the liturgical books approved by competent authority are to be observed faithfully; accordingly, no one is to add, omit, or alter anything in them on one’s own authority.
Changing from standing to hand holding during the Lord’s Prayer would be an alteration or addition of something provided for in the liturgical books and thus would be at variance with the law.
