I'm thinking about purchasing the Buiness dropbox for our small company. We are all Mac based and use the Adobe Creative Cloud programs. Can I link images directly to the online dropbox storage through Indesign and illustrator?
Practically speaking... no, you can't. At least not in the way you're intending.
You may be able to embed a web image into a document (assuming InDesign supports that, I have no idea), but to do so you'd have to create a Dropbox share link to each and every image you want to link to and then modify the share link so that it results in the raw image.
I suspect the method you're using is intended to link to files local to the document (same computer, network share accessible to the comptuer, external drive, etc.), and not meant for linking files from the web.
If I save my images that I'm linking to via InDesign on my desktop the links will break when I share my file to others on my team. I'm wondering if I can link directly to the cloud.
It may be something that is coming in the new Extensions set up, but, no, I dont think you can save directly to the cloud and work on files inside Dropbox on the Adobe Cloud.