You can use SMEStorage's CloudDAV service to get WebDAV access to your DropBox. WebDAV is one of the import/export options in Pages and the other iWorks apps.
SMEStorage is a cloud storage aggregator. It lets you combine various cloud file services in one place. The free account lets you add two cloud services, and DropBox is one of them.
The only real problem with this approach is that files you add directly to DropBox (bypassing SMEStorage) do not automatically update on SMEStorage's servers. You need to force the refresh either at the website, or using the iSMEStorage app ($4.99). It works beautifully for uploads. You just need to remember to force a refresh in SMEStorage before looking for files to download. Or you can just use the DropBox app for when you download.
The other downside is that it makes for a much more complicated file structure. You may have to poke around the first couple of times before you find the right place to upload/download your DropBox files.