I think so. At most, the Pope would just issue a statement condemning the war, like JPII did with the 2003 Iraq invasion, but he likely wouldn't enforce it to any significant degree.
Now, if he DID enforce it with actual excommunications, it might have some signficant impact. But that's so far removed from the way the Catholic Church operates these days, you're basically asking us to imagine that it's a different institution.
I did read somewhere that Paul VI was more dovish on Vietnam than a lot of right-wing American Catholics(eg. Cardinal Spellman). An interesting thing to note is that, despite the caricature popular in some left-wing circles of the Vatican and the USA being in lockstep(which might have been a valid view during the Cold War), they actually have some pretty antagonistic interests. The Vatican didn't recognize Israel until AFTER the PLO did, for example. And I'm guessing that their opposition to the Iraq War was motivated at least in part by a desire for the Baathists to remain in power, given that that party was the one that protected the Christian community in Iraq.
Obviously, neither of those positions were in keeping with those of the neo-con Israel lobby or their Bible Belt fundamentalist allies.