Again, no one can make a great prediction because there is just not enough info available. With that said... If you were to buy a PR 3 with close to 8k starting salary for a decent price, and assuming PR manager influence is calculated as a percentage of base merchandising profits, and assuming that my very small sample is a good representation of the range of increases, and assuming that there is not an increase cap, and assuming there are no other crazy things going on, I think it would be a worthwhile investment that you could profit from in as quickly as your second season.
The obvious problem with making a suggestion like this is the huge lack of data, and this could easily cost you a lot of money as well. One thing is for sure, in almost no way can I estimate this resulting in a profit during your first season. Unless you feel like taking a risk and experimenting for multiple seasons, I really don't recommend buying anything higher than a PR 2 for the specialty. I have no idea what to say about higher level PR managers influence because I haven't ever seen any data on them. The most I have seen are just people saying, "yeah they are nice and make me money" with no specific data to validate that or understand the actual effects.
I only assume that odds are against you promoting this season because according to your league standings you are currently 5th ranked overall. Odds are usually against a lower ranked team in the playoffs. Sorry, I tried to be clear that this was only an assumption based on your standing.