we have cruised 5 times on an itinerary that stops at CC.... this means I was silver for many of those cruises. 4 of the 5 times, we were able to book online either immediately at the time of our window opening, or by stalking the site several times a day looking for a cancellation. The 5th time, immediately upon embarkation, I headed to the excursion desk and placed myself on the wait list, and received news the next day that we had a cabana assigned.
We have never sailed concierge- so yes it is TOTALLY possible!