From the looks of it, this is possible through the use of the Quickbooks SDK and QBXML.
The server can pass requests and receive replies through standard XML. So with the use of a parser in PHP, this is entirely possible. There are several caveats with this, all of which i am still trying to figure out. It does seem to be much easier to intergrate with Quickbooks Online, but it is possible with Quickbooks as well.
I will post more on the subject when I figure it all out, but you can also check out the SDK available as a free download from Intuit's developer section.
cheers....