If you already have automator running (as it appears), then your notification script would need to save some context around the notifications. (I don't know of a direct means to delay and to "batch" the default event triggers; the rules fire for each upload.)
Another option would be a cron or periodic or launchd job that goes looking for the contents of the folder periodically, and sends along notifications for all of what it has found new, and then relocates the files into another directory or such; out of the dropbox folder and into a staging directory. The example I have of this stuff is a periodic-based job that does a nightly dump of a MySQL database, which is probably not what you want.
The other approach would be to automate the whole workflow and tie it into your local web services, and have a part of the web site that allows the client to submit files and get them uploaded, and that then handles the uploads, staging of the files, naming of the files, and notifications.