HRC does allow walk ups but clubs can control this by not allowing it. It is pretty simple. Some clubs will charge an additional fee for walks up in Seasoned and Finished. This does not make bird counts simple but there are ways to work out the costs. Remember the CLUBS control this along with the limited number of dogs in each flight as long as the don't exceed the rule book qty.
To the O/P- run your dog all day as long as you don't have a gun safety issue and you don't feel you are undermining your training. In finished we don't usually see folks run if they are out but if they are new to the program and need more line time they will run in the afternoon. Sundays is pretty much a given that if you are out most will head home early and not run.