I've always liked the idea of PBYs in game, I see them as having 2-3 purposes:
1) Carrier resupply. I think it would add more depth to CV battles if there was a line of resupply coming in for both sides to consider as well. More than likely this would require some tweaking so people wouldn't just be flying C47s out there (slightly faster right?). On a bit of a side note, maybe alter the damage to a carrier to allow ords to be destroyed in some manner.
2) Recon. Someone came up with this idea and I found it really interesting. The ability for PBYs to mark positions and directions of enemy carriers for a pre-determined amount of time. So when someone flies over an enemy carrier, that location and direction is visible to friendlies for 5-10 minutes (or even just while the PBY is within a certain range, encouraging the PBY to circle to keep the location visible). Other planes would be faster but a marking on the map would be much more accurate and effective (IMO).
3) Ords, maybe. This would be something up for discussion, could outfit the PBY with small ord load, but wouldn't be a necessity (until we get subs!).
PBYs could launch in a way similar to PTs boats off of coastal bases, although probably would have to have a separate launch point for the PBY by itself. The downside is that this requires a lot of little changes (how CVs work, new supplies, the recon thing, the launching) for one plane. IMO the PBY would be used enough to justify the changes, but I'm not in charge of those decisions.