I have seen this in newer 3300 softwares with analog trunks as well (and one PRI, but that is a different issue that I think is related to something else with a certain carrier), the internal IP phone answers and there is about a 2 second delay before audio cuts though to analog trunks... The best I have found is to make sure the Line Quality Test is done and the result set on the lines accordingly, Caller ID is set properly for each trunk, and it get better but I have not been able to get rid of the delay completely.
Seems to have started in version 4.2, is still in the current software revision, and only appears on CX-variant platforms, I have not seen a single MX-variant with this issue. I opened a ticket with Mitel on it once, but got tied up on other issues and it auto-closed in the system, most customers have just gotten used to it and don't complain anymore, but it is annoying. Pretty sure I checked that COS for that option Ralph mentioned, but I might be wrong.