Even if you ran pgbouncer on a different box, the situation is still better. Suppose you have a probability P of having a partition between any two boxes. Then the probability of a partition taking down the system with pgbouncer is P.
If you instead had N clients coordinating among themselves how many connections to use, your odds go way up. The probability of a partition existing between two clients is 1-(1-P)^(N(N-1)/2) ~= N(N-1)P/2 (for very small P). Once two clients can't communicate, neither one can connect to the DB (because they don't know if the other two have pushed the db over the limit). All clients will need to stop connecting to the DB if any client is ever disconnected from the other N-1 of them.
In a distributed system, ensuring that SUM(x[i]) remains bounded for all time is a tricky problem to solve.