Is it required to have the AHCI driver installed and enabled to use an SSD?
Without knowing for sure, I'm gonna say it's not required but a good idea. Unless you absolutely need IDE mode, you might as well enable the additional features of AHCI mode under any configuration. Start By Enabling AHCI (With TRIM) Benefits Of AHCI Quote form First Link
The short answer is no. I have an SSD as my boot (Windows 8 OS) drive and it is currently set as "Native" (SATA / IDE). I've tried both and have noticed no real performance boost so I decided that I really didn't need the extra features (hot swapping and Native Command Queuing) that comes from enabling AHCI mode. But again, that's just me.
Windows has had an AHCI driver built into it since Vista. Installing Intel's AHCI driver can bring performance improvements, but some manufacturers recommend using Microsoft's built-in driver when flashing the SSD. AHCI is recommended for SSDs regardless of whose driver is used. NCQ can decrease wear and increase performance on intensive workloads, at least when the SSD controller is capable of taking advantage of larger numbers of parallel operations (aka queue depth). AS SSD is a good test for this.
Yep native command queuing is a performance factor in server type environments and in instances involving I/Os from robust multi-threaded applications, however your typical desktop user is not likely going to really notice these performance increases
