According to the MSI page for your board
here, the K9AG does support the Phenom X4 processors since bios version 7368v17. This bios update, if you do not already have it, can be found
here. You will need to update the bios before you install the new processor, without applying this update the pc will likely not boot at all.
All AMD Phenom X4 processors are classed as "AM2+" and any AM2 or AM2+ motherboard with the right bios support will support these chips. The 690G chipset does support the Phenom X4 processors, but as it is not an AM2+ chipset, it will only support a bus speed up to 1000 MHz, while AM2+ native chipsets will support the full HT3 standard up to 2600 MHz. Note this does not effect the speed of the processor in any way (a 2.4ghz Phenom X4 will run at 2.4ghz on either platform). The reduced HT speed may have a small impact on performance but I've yet to see it show any significant performance degradation.
As for "is it worth it", it really depends. Very few games really benefit from quad core processors in terms of raw fps. The ones that benefit the most simply offload additional threads for AI or Physics to another core, or use the other cores to prepare upcoming threads. So this can have an impact on load times and things like that, but generally speaking its minimal.
If you use a lot of software that is optimized for multicore processors such as software dealing with 3d modeling/rendering, or audio/video encoding, then the gains will be substantial and in some cases may cut the processing time in half.
Beyond that really all you'll gain is multi tasking abilities. For example I can be running Folding At Home, encoding an Mpeg, scanning an Mpeg, and burn a DVD while I'm in the middle of playing Left4Dead and it doesnt really effect my performance in any significant way.
So if your bios is up to date and you feel you can benefit from the upgrade, then yea you should be just fine. But I would suggest holding off a little longer as the Phenom X4 II processors are going to be launching in January, and will be a good bit faster than current Phenom X4 processors. These will likely retain the same support with AM2 motherboards [that have the right bios version] and would be a better route. Beyond that, you have the new AM3 processors launching in the end of the 1Q, and will essentially be the same as the AM2+ version [of the Phenom II X4] but will have a wider selection of speeds. The AM3 Phenom II X4 processors will require DDR3 memory. The AM2+ Phenom II X4 processors will require DDR2.