If windows, "classic" runs at priority 4 while the BOINC-version runs at priority 2, so "classic" gets 99% of the cpu-time... But it should be possible to run latest version of seti-driver at lowest priority, and by this method have "classic" run if no work from BOINC.
Of course, if you also "attachs" to Climateprediction there's no risk of running out of work. 
 
To get any work in BOINC, you need to "attach" to a project.
Returning work in BOINC is a 2-step-process, step 1 is uploading result-file(s). This normally happens immediately after a result is finished crunching, and afterwards the gui lists that WU as "ready to report" in the work tab.
The 2nd step is to "report" finished work, and this happens when your computer successfully connects to a scheduling-server and all "ready to report" WU are removed from the work tab in BOINC.
To minimize traffic on the scheduling-server, they're trying to group multiple "reports" together, so you only connect if either you're asking for more work, at least one result is near deadline, or you manually hit "update" on the Project tab in BOINC.