Let us assume, for the sake of argument, that all six of the disputed Paulines are indeed Pseudo-Pauline. There is often an unspoken supposition that they must then have been written subsequent to Paul's life. This does not in fact necessarily follow. There is no reason in principle that one or more Pseudo-Pauline texts might have circulated prior to Paul's passing. Indeed, there are hints within the undisputed Paulines that Pseudo-Pauline literature had begun to circulate during his lifetime: cf. 1 Cor. 16:1 and Gal. 6:11, in which Paul goes out of his way to indicate that he is writing in his own hand; 2 Thess. 2:2 refers to letters sent "as if from Paul," thus suggesting an awareness of at least the possibility of spurious letters, whilst 2 Thess. 3:17 explicitly spells out that Paul's signature is a mark of authorship, and although the letter is disputed we should not be surprised if this reflects an contemporary or near-contemporary awareness that Paul had such concerns or engaged in such a practice. What this means is that merely establishing that a letter is Pseudo-Pauline does not establish Paul's death as a terminus post quem for its date of authorship. Of course, the opposite would the case: if it can be shown that the letter could not have originated prior to Paul's death then it must be reckoned as Pseudo-Pauline. Pseudo-Pauline origin is insufficient to establish a post-65ish date, but a post-65ish date is sufficient to establish Pseudo-Pauline origin.
So perhaps the thing to ask is whether any of what we are treating as Pseudo-Pauline texts clearly post-date Paul's life. Probably the main argument used to establish that certain of these texts must post-date Paul's life is what we might call the argument from ecclesiastical anachronism: i.e. the ecclesiastical structures evinced in some of these texts is more advanced than that which existed prior to c. 65. It ought to first be noted that this is really only relevant to 1 Timothy and Titus. And when I look at these texts I'm really not convinced that the argument holds. Yes, Paul talks at length about the qualifications of bishops and deacons in 1 Tim. 3, but Philippians 1:1 supposes an identical bipartite church structure. Yes, 3:2 refers to "the bishop," τὸν ἐπίσκοπον, but is a single definitive article really sufficient to establish that we are dealing with a monarchical bishop here? The author elsewhere talks about elders, even though he doesn't deal with their qualifications in chapter three, which leads me to suspect that we are dealing with the well-attested, early tendency to treat the offices of the bishop and elder as interchangeable. This perhaps receives some confirmation from the fact that Titus 1:5-9 talks about the qualifications of elder in a way markedly similar to the way in which 1 Tim. 3 talks about the qualifications of the bishop, and again this discussion does not seem to reflect an ecclesiastical structure more advanced that anything in the undisputed Paulines. As such I'm not entirely persuaded that the argument from ecclesiastical anachronism is empirically sound.
A stronger argument with specific respect to 1 Timothy comes from 5:18, which quotes as a γραφή a passage identical to one found in Luke (cf. 10:7), and only found in Luke. Given the tendency of early Christian writers to cite quotes inexactly from memory the fact that it is verbatim identical is really quite significant. Although one cannot rule out that we are dealing with an otherwise unknown text, including a hypothetical source for Luke's Gospel or a proto-Luke, by far the simplest and most compelling argument is that 1 Timothy is citing Luke's Gospel. Now, the fact that it is referenced as a γραφή does not tell us a great deal about the date of the text: we have no positive evidence telling us that Christian writers couldn't have begun referring to Luke's Gospel or any other writing as a γραφή soon after it was written. It just doesn't seem sufficient to establish a terminus post quem. The real issue comes with what one thinks about the date of Luke's Gospel. If one dates it to post-70 then one would most reasonably conclude that 1 Timothy also must post-date 70, and thus subsequent to Paul's life. If one follows the "early chronology" for Luke-Acts that would see Acts being written at around 63 or 64, and Luke's Gospel sometime before that, then a 1 Timothy written during Paul's life becomes a possibility. This is simply another reminder that questions about the dates of the New Testament are as a rule quite intertwined: a shift in the date of one text can have definite consequences for the date of another.
Frankly, I can't think of any real reason that any of the other Pseudo-Paulines must post-date c. 65. Thus I conclude that of the Pseudo-Paulines only 1 Timothy could not have been written during Paul's lifetime, and this only if Luke's Gospel is dated subsequent to Paul's life. Again, though, I must emphasize: these are not arguments for Pauline authorship. A pre-65 date or even just the possibility thereof is insufficient to establish Pauline authorship. And the statement "Could have been written during Paul's lifetime" is not identical to "Was written during Paul's lifetime." But we should be at least open to the possibility that one or more letters of the canonical Pauline corpus are precisely the sort of forgeries against which Paul perhaps was taking precautions by putting his signature on his letters.