Hi recklasman,
Though Dell has not tested the power supply you intend to purchase, however, while researching on this topic, I saw a successful upgrade of power supply to Antec Neo Eco 620C on a Dell Inspiron 620 MT which is bigger than the Corsair CX600 in dimensions.
Dimensions of Antec Neo Eco 620C : 86mm (H) x 150mm (W) x 150mm (D) ; 3.4" (H) x 5.9" (W) x 5.9" (D) [as given on manufacturer website]
Dimensions of Corsair CX600 : 86mm (H) x 150mm (W) x 140mm (L) ; 3.4" (H) X 5.9" (W) x 5.5" (L) [as given on manufacturer website]
Refer to the screenshot below in which the Antec is installed in Inspiron 620 MT
