As you stated, the Nvidia chipset does not support AHCI mode, however, after installation check in Device Manager to ensure that the Microsoft generic driver is installed for your storage controllers vice the Nvidia controllers.  To install the Microsoft controller, try these instructions:
1.  Go to Device Manager and find "Storage Controller" and click it.  There will see three nVidia controller drivers. You will need to replace each one with Microsoft’s "Standard Dual Channel PCI IDE Controller".  To do so, right click on one of the controllers, then click on Properties, then click "Update Driver".  Next, click "Browse" for drivers, then click “Browse my computer”, then "Let me pick".  You should be presented with a pop-up, and you should see "Standard Dual Channel PCI IDE Controller" from Microsoft as one of the choices, and that is the one to select. 
2.  Repeat the process for the other two Nvidia controllers.  Once you have changed all of the Nvidia controllers to Microsoft controllers, you will be required to reboot the system to implement the changes.
After you reboot, you should check the controllers in Device Manager to verify that all of the changes were implemented.  To do so, go to Device Manger, then click IDE ATA/ATAPI Controller, and you should see the Standard Dual Channel PCI IDE Controller drivers.
3.  By installing the Microsoft controller, you should also be able to use TRIM, as long as the SSD is not part of a RAID array.  Good luck!

IMHO, unless you purchase a controller with processing and RAM on board, which are expensive, I would not bother. The cheaper SATA III cards don't really provide much better read/writes than the on board controller.