It's not going to damage the CPU. It is possible it will damage the motherboard, BUT the Sabertooth 990FX is a high end motherboard with quality components and design, so there is a high likelihood there will be no ill effects, and will be no different than running a highly overclocked 8350.
Rev 1 does NOT support the 220Watt cpus,
Rev 2 does
GEN3 R2.0 does
And the new R3.0 Does.
Like BZ said,It Should be ok,But no Guarantee,
However the Sabertooth boards are rock Solid.I just sold my Rev 1 and picked up a rev 3.0.
You should just sell off the 9370 and pick up a 8350 or 8370 instead.Less power(consumption)/less heat.
Each mobo maker lists on their website exactly what model CPUs/APUs are supported by a specific model and REV. mobo. The reason that your mobo does not support the FX-9000 series CPUs is because these CPUs require at least 220w of power - almost twice the std. FX-8000 series 125w CPUs. Your mobo is almost guaranteed to burn out due to the excess power required by the FX-9000 series mobos and it could definitely damage the CPU. In fact you are likely to also start experiencing BSOD, reboots, etc. as the mobo power supply (VRM) to the CPU is NOT designed to deliver the power required under heavy loads.
All of the popular aftermarket mobo suppliers sell mobos specifically designed for the FX-9000 series CPUs. IME Asrock has some of the best AM3+ mobos available and at excellent prices. You can't afford to cheap out on a mobo, PSU or HSF for the FX-9000 CPUs due to the 220w power requirement. That means you also need a HSF or other cooler that provides a minimum of 220w cooling. It also means you need a PSU with a minimum of ~54 amps. power on the 12v rail(s). You will also likely need a small fan cooling the VRM circuit of the mobo, especially if you do not use a HSF for CPU cooling.