Any way to prevent Dropbox from opening the Camera Uploads folder when an iPhone is connected?

It appears there is no known way to stop this behavior. I asked Dropbox support about it and got this response.

Thank you for this feedback. This is part of the functionality of camera uploads so unfortunately there isn't a setting to turn this off; thank you for your patience with it. I will pass your feedback onto our Client development team.

Not sure if this is the setting you're looking for... However if you go into your dropbox preferences ... You can see this setting:

If you uncheck the final option

All should be well and you should not get bothered by dropbox.

Hope this helps.