If there are newer chipset drivers that offer features supported by the motherboard you DO have, the manufacturer will generally list them on their website. Other drivers that might WORK with your chipset, but contain features that will really only benefit newer hardware, are what you're likely to find on the Intel or Realtek, for example, websites. Will they work, probably. Will they offer any additional benefit, maybe, but probably not. It probably doesn't hurt to try them, but if you start experiencing unexplained issues, I'd revert to the older drivers right away. In some cases there might be improvements even on older hardware.
If you install newer hardware that your current chipset or bios do not support, then it's usually a good idea to upgrade to the newest BIOS and chipset drivers. Unless the hardware is really old, I don't see a problem with upgrading unless there is a specific footnote saying it doesn't work with your chipset.