Hi Justin,
The disassembler will publish already ‘disassembled’ body messages to the database. It will not wait until the complete interchange has been processed. Everytime the GetNext method of the disassembler is called and not returns null a message is published to the database.
Make sure to implement a streaming approach in your component. Return a body message a soon as possible.
The delay in your case can indeed be caused by lack of resources on the BizTalk server. You can use performance monitor to find out if and why BizTalk is throttling.