It seems to me that a new SATA optical drive wouldn't cost much more than the adapter, unless you already have the adapter.
the adaptor only costs £2.10 from ebay, or £3.20 from a UK seller. so it would be cheaper than buying a whole new sata drive.
The fastest PATA can go is 133M/s regardless of whether the adapter can go 1.5G/s or not. Save your lunch money for a week. Shop around. You can find Double sided DVD burners for under $25 every weekend.