I agree that trying to run a 4870 on that PSU is asking for trouble. If it was say something like a Corsair VX 450 Watt PSU that has a single PCIE connector but a solid single 33Amp rail then i would say fine go for the adapter.
However your PSU (if google gave me the correct one) has 2 16 Amp rails which does not guarantee it has 32 Amps, i would be very worried that it was over stating itself, it basically means it can deliver 16 Amps on either rail but doesn't mean it can do so on both at the same time.
A good quality PSU would list the Wattage for the +12V rail/s and if you divide that number by 12 you get the true Amperage of the +12V rail/s. With a good make this will equal the given Amperage on the sticker, lots don't even come close.