Yes we've ran into this issue and no it is not typical. Just to get an idea with the 2.13.1 agent.
After logging in and attaching the writable it takes up to 2 seconds to process the appstack (not starting up application or merging registry keys, reverse replicate is done after logon is complete).
Normally if you see a 3 minute gap it means the appstack is waiting for the timeout to expire. When attaching an appstack it normally is done within a few secs but with older version or a corrupt appstack it can take up to 180 seconds before it is attached.
I would attach during logon and then check the svservice.log file to see if there is some strange behaviour. Could you please post outcome of that here?
