Large number of short lived connections - could a connection pool help?

We have anywhere from 60-80 background worker processes connecting to
Postgres, performing a short task and then disconnecting. The lifetime
of these tasks averages 1-3 seconds.

I know that there is some connection overhead to Postgres, but I dont
know what would be the best way to measure this overheard and/or to
determine if its currently an issue at all.

If there is a substantial overheard I would think that employing a
connection pool like pgbouncer to keep a static list of these
connections and then dole them out to the transient workers on demand.

So the overall cumulative number of connections wouldnt change, I
would just attempt to alleviate the setup/teardown of them so quickly.

Is this something that I should look into or is it not much of an
issue? Whats the best way to determine if I could benefit from using a
connection pool?

Thanks.