I’m not sure how much that argument is going to hold up given that Timothy is mentioned in Acts (several times), 1 Corinthians, 1 Thessalonians, and Philippians, and Titus is mentioned in Galatians.
However I don’t think the point was to say that Sts Timothy and Titus never existed in the first place, but that they were used as covers in falsely attributing these letters to Paul.
Most allegations that certain letters in the New Testament are falsely attributed to Paul are based upon stylistic differences between letters. Now on the face of it this doesn’t seem like much of an argument to overturn the universal witness of Christian tradition that 1&2 Timothy and Titus were written by Paul, especially when the early Church was keen on rooting out false letters and gospels.
One could just as easily explain differences in style for these letter as based on their being personal letters to church leaders instead of public letters to young converts. As if a man as well educated as Paul could not have the ability to write in a different style. Another thing to note is we don’t really have that much of a sample size in Paul’s letters to be making comparisons of style and trying to find out true pauline style in them.
If you are interested in defenses of Pauline authorship, the Ignatius Catholic Study Bible - New Testament by Scott Hahn and Curtis Mitch has short essays on authorship of every letter in the new testament, and you could find very in depth defenses in the (baptist) New Testament textbook
The Cradle, The Cross and the Crown by Andreas Kostenberger et al.
Or these this online source:
tektonics.org/ntdocdef/pastorals.php