It's amazing what a difference a backwash can make for the functionality of the main filter/pump system. A modest increase in pressure can lead to a significant decrease in flow rates, as I just observed last weekend. Our pool had been starting to get some spot algae (yellow/mustard) on the walls, and I kept adding lots of chlorine. I would brush every day, and yet it kept coming back. I noticed that the MX8 autocleaner was acting listless. Despite cleaning it out, it remained listless. So, I backwashed and the pressure dropped from 25 to about 15. I didn't want to break the filter down, so I did my typical backwash where I cycle the filter valve between backwash and normal about 3-4x. This tends to get nearly all of the filter media pumped out. I then restocked the filter with cellulose DE replacement. I couldn't believe the difference in flow rate. The MX8 sparked back to life and the skimmer and surface flow both looked much better. I'll try to be a little more cognizant of this.
If backwashing doesn't fix this, you might have a pump issue, or there could be something trapped in the vacuum line. Does your pool have an attached spa? If so, do you see that moving the suction side 3-way valve to the spa line affects the flow? Do you have a drain vs. skimmer valve? If so, do you see a difference in flow rate by moving that valve from one side to the other? If you do, this would suggest a clog in the skimmer vacuum line. If not, I'd be checking the pump to ensure that the impeller is in good shape.
To answer your question, yes, the skimmer typically has enough flow to connect up a pool vacuum and clean the floor and sides.