Any SSD is faster then a regular hard drive, however, if the computer can't push the data fast enough it will be somewhat pointless. You will be very limited by the bandwidth the CPU and Ram can handle.
Additionally,modern SSDs thrive on SATA III 6Gbps, and are fairly good on SATA II 3Gbps. I wouldn't recommend hooking it up to a SATA I 1.5Gbps based computer. The fastest standard hard drives could saturate that.
Oh, and to add, AHCI is necessary for all the modern functions of an SSD such as trim and wear control. A controller without AHCI will limit some of the performance (and may prevent booting an OS in some cases)