Well,it would work,----- BUT!!
If it is designed to be hard wired to the Mains Supply, enclosed in a double insulated enclosure,& dedicated to supply power to some device with no wired connections to the rest of the world,other than the incoming Mains,it would be OK.----,of course,all dependent on the approval of the Regulating Authority.
Somehow,though,as it is in the "Beginners" section,I doubt if that is the case.
As a bench power supply,it has several problems:-
(1) Mains Active & Neutral
can be transposed at power sockets.
If they are,Active is connected to your "common ground" on each negative half cycle of the Mains,making it "hot" with respect to Mains Earth------you can get "'zapped"
(2) If the situation in (1) exists,& another device with its "common" connected to Mains Earth is connected
to your power supply,the bottom diode of your doubler shorts the Mains supply on negative half cycles ----Goodbye diode!!!
(3) If you manage to get your Mains connections correct,& connect another device as in (2),you will short out the bottom capacitor of your voltage doubler---"zap"