I think it it would be easier to pass and possibly more effective to have a law that said that employers were immune from any liability resulting from guns in the work place.
I think many employers, especially for really large companies, mainly ban guns because they are afraid they will get sued out of business.
The generic statement you propose would probably just be ignored by the businesses and the courts right now since so many people don't consider carrying a gun a right, even though the US supreme court ruled that owning a handgun is a right.
If a company bans carry you could find another company to work for, become self-employed, or take the risk of being fired for violating company policy. Right now of course not many companies would allow employees to carry guns.
If they can still ban carry on company property while working then being able to have it in a vehicle is not all that great. What are the odds that they would discover a firearm in your vehicle anyway? I figure if they are going to be that intrusive into my personal property I don't want to work for them anyway.
I'd also like to see a bill for carry laws where you could carry concealed without a permit like in Vermont and Alaska. And I think we need a law like they have in Utah which forces all public universities to allow firearms. In the case of the University it is actually illegal to have a firearm in your vehicle on their property, which effectively uses the law to take away your rights even when you aren't there if you did have to go there at some time and decided to park on the property. Violating the law would result in a criminal offense, which I think is much worse than being fired at a job.
Actually the best way to implement what I just said is to completely repeal NRS 202.350 and NRS 202.265 and all other laws relating to carry and forbid (or strengthen current laws that forbid,) any government agencies from regulating firearms. There should be no criminal offenses and no academic sanctions from public institutions.
If there is going to be a permit system in place it should only exist for the purposes of maximum reciprocity with other states and not be a requirement for carry. I guess that isn't such a big deal though considering that we can get non-resident permits from other states.