Internet connection for Adobe

I use Premiere Pro, After Effects, Photoshop, Audition, and occasionally other Adobe apps, but don't use any cloud storage or syncing. My performance is fine.

I have a slow DSL connection (1-3 Mbps).  Downloading updates takes a while, but I do those manually overnight.

using adobe's apps does not utilize any internet traffic.

installing adobe's cc desktop app and programs, updating adobe's cc desktop app and programs and using adobe's cc services (eg, synching local files with adobe's cc servers) uses your internet connection

the 2 previous commenters above address issues arising from the 2nd paragraph, but i have a sense that you may be concerned about using adobe apps (eg, id, ps, ai) and the first sentence addresses those non-issues.  ie, you should have no problem using adobe apps.

periodically the cc desktop app checks to see that your subscription is current, but that is episodic (once per month with a monthly paid subscription and once per 100 days with an annual) and engenders little traffic even when it occurs.

Bear in mind the software installs, including updates are often over a gigabyte. This may take a lot of time. Saying it is ADSL will not tell you whether it will be a good experience, as the speed can vary a lot - according to distance and how much you pay - just like other forms of broadband.

You should be fine, unless you want to download/upload assets on the cloud. I would say either disable automatic updates in Creative Cloud App or disable the launch of Creative Cloud App at login. Infact you should be able to use the applications offline as well for around 90 days.

-Manan