After rearranging the mass-models, just for the sake of the exercise (Eric Storm’s suggestion), I’ve computed the fastest time to Alpha Centauri via a Mag-Sail equipped Two-Stage “Daedalus”. In this case both stages will be use to reach the cruise speed, then the mag-sail will be deployed at the appropriate point in the voyage. The minimum trip-time is when the cruise-speed is 0.13488c, the mission time 45.82 years and an initial mass of 181,480 tonnes. So, yes, Alpha Centauri can be reached in under 50 years by “Daedalus”. Interestingly exactly 50 years needs a mass of 66,040 tonnes (this includes the 1,000 tonne mag-sail.)
How far can it reach in under 100 years? About Tau Ceti’s distance – 11.9 ly. To reach GJ 581c requires ~152 years and about 540,000 tonnes initial mass, minimum. For the same mass as the minimum time to Alpha Centauri, the trip to GJ 581c takes 164 years. Patience is required, it seems.