Well, I don't recommend this. I think the minimum time before a connection is discarded due to timeout is 1 minute, so you have an opportunity to use up a really lot of connections.
I assume from your "no managed cx available" message you are using a jboss 3+ version. I'm surprised you're running out of connections since the max is per user. Perhaps you are running out on the pool that actually has connections that do the work?
David, I faced running out connection (getting from the pool). The case is that for each call to a CMP bean, a new connection is created (from v$session in oracle), and that connection is marked INACTIVE. However, it wasn't cleaned for a long while (e.g. one day). You say 1 min., how to set it ? I am using JBoss 3.0.3 and Oracle8i, with oracle-service.xml.