Well, the answer I would say is, it is quite do-able but that sort of commute will test your stamina to the utmost. Do a few trial runs at weekends or on days off, just to see what it feels like! It's impossible to predict the timing because all cyclists are different.
Basically you have four ways of getting across the South Downs. One is just to follow the cycle track alongside the A23. From Patcham northwards it's segregated from the D/C, reasonably well surfaced and clean (last time I looked!). Indeed quite feasible as cycle tracks go. You can follow it (becomes the B2118) as far as Sayers Common, where I'd suggest you leave the A23 and continue on minor roads.
The second option is to leave the A23 at Pyecombe and take the A273 over Clayton Hill. A fairly easy climb but the road is heavy with traffic in the rush hours, it depends on whether you are comfortable with mixing it with the motorised commuters.
The third and fourth options are Saddlescombe (Devils Dyke) and Ditchling Beacon, respectively. Both of these are challenging, if you want to do them daily! I used to commute over the Beacon, but never daily and never as part of a 25-mile commute (my commute was 10 miles in those days) - and I was a whole lot younger and fitter! And I often chickened out and took the easier Clayton hill. And sadly, both the hilly routes have become notorious rat-runs in the peak hours (the FNRttC boys only see them in the wee small hours). I would think carefully before choosing either of these.
Once you're north of the Downs, picking out a route along minor roads is easy and you'll be less bothered by traffic. Go to Google Maps and pick roads in yellow or white.
