Yes restarting Cumulus, running on a computer connected with a Davis USB datalogger to console, will download from the logger the data since Cumulus was last running - i.e. shutting down Cumulus and the computer at night and restarting in the morning, Cumulus will download from the logger the data since last night's shutdown. Cumulus monthly log files will be updated with the downloaded data.
With the 'catch up' setting in Cumulus turned on, Cumulus will also upload the data to Weather Underground. It would also do the 'catch up' to PWS, Weatherbug and WOW if you had Cumulus uploading to those sites.
The same thing would happen with a serial or IP logger.
Davis stations can run stand alone, or connected to a computer or router which would then need the optional logger. Once connected to a computer then Weatherling program or third party programs like Cumulus can access the logger and the live data.
You will like the Davis!
Enjoy,
Paul