Using the frame ground on the genset won't change your HZ at all. HZ comes directly from engine speed. If you have a weak engine or a cheap crappy governor on the engine, your HZ won't stay stable. If you're looking to maintain really stable HZ, you will want to upgrade to a more expensive unit that has an electronic governor.
The genset frame ground on portable gensets is only to ground the genset frame to earth ground for added protection against shocks if the generator happens to short to ground. If you wish to hammer a 8' ground rod into the earth for the added safety, go for it. Wish you lots of luck getting it back out of the ground if it's not a permeant site.
As far as induced electrical noise, I've never had those issues with any of my unearth grounded portable gensets. Earth grounding your genset may solve this issue, but will never do anything for your HZ. This would probably be an issue on cheap gensets.
If you're having a lot of trouble with your HZ, your governor may need adjusted for droop/sensitivity, and or engine speed. A good no-load HZ is 61. 8HZ than load the genset and it should ride about 60HZ. If not you can fine tune from there. Never adjust your governor with any loads on the genset or you may fry something. Never adjust your governor by RPM, always use a meter on the HZ setting!!
2-pole genset=3600 RPM=60HZ
4-pole genset=1800 RPM=60HZ
Earl