Dropbox and the Dropbox API do offer the ability to upload files, so this should be possible.
If you want to do this just from the Dropbox app itself, without using the Dropbox API yourself, you should look into setting up shared folders as needed and inviting the guests: https://help.dropbox.com/files-folders/share/share-with-others Guests can then upload their photos to the shared folder via the official Dropbox app.
If you want to use the API to build your own custom app, you can accomplish this, but exactly how you do would depend on how you want this to work. Based on your description, it sounds like you're probably thinking of one of two main ways you might do this:
Much like the non-API option above, you can have each guest connect their own Dropbox account to your API app, and once they do so you can add them to a shared folder and upload photos to that shared folder. This would require them to have their own Dropbox account and authorize your app, but you could streamline the process since you control the code.
Alternatively, you may be thinking of a setup where the guests don't each have and connect their own Dropbox accounts, but rather you just always connect to one predetermined Dropbox account (so a shared folder isn't necessary).
The API was designed with the intention that each user would link their own Dropbox account, in order to interact with their own files. However, it is technically possible to connect to just one account like this. The SDKs don't offer explicit support for it and we don't recommend doing so, for various technical and security reasons. This especially applies to mobile apps, since client-side apps can't secure secrets from malicious actors.
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