^^Yes. In addition to the current information, bank statements, pay stubs, etc., I made a separate tab in my application packet for my proof of cohabitation for 4 years. I included my tax returns from the last 4 years - nothing special, just my downloaded turbo tax forms. I do have bank statements from over the last 4 years, but that is a ridiculous amount of paperwork to send in, so I just had each of our banks write a letter on their letter head stating we were joint account holders for x amount of years. And I included our rental lease that was signed in 2003. That was it. No photos, or our daughter's birth certificate - these things don't prove cohabitation anyway.
I really don't think you will have an issue if your documents are starting from August 2004. I certainly didn't look for documents that were exactly 4 years old. All I thought about was finding something from 2004, 2005 and so on.