It is definitely possible to do the network in one day, because I've done it in the past, using an GM Wayfarer (same time restriction on trains as a normal Ranger, but wider area, allowing connections via New Mills, Wilmslow and Warrington if required, and no time restriction on buses, allowing positioning moves to be done before the 09:30 start time), using Bramhall as my starting location.
There is, unfortunately, no peak time S1 tickets allowing travel on trains.
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Actually, having looked through the timetables, it appears to have become almost impossible to call at all the stations in GM (which is how I judge 'doing a network') on a GM ranger/Wayfarer (excluding Saturdays), because it would be impossible to get both Clifton and Ardwick without getting extremely lucky with the 219 bus from Ashburys to Piccadilly Gdns, and being extremely quick on your feet to get to Victoria in time for the 17:36 service to Clifton. If doing it on a Saturday, you can do Ardwick in the Morning, and Clifton in the evening (or vice-versa).