Legality aside, I'd also argue that the sign is putting the public at risk.
Consider this - I drive a Jeep. If I were to leave my firearm in my vehicle, there' really no way that I can make it "secure". I can meet the letter of the law, sure, but even if I have a safe bolted or attached to the tub with a steel cable, it would only take a pair of bolt cutters or maybe a small crowbar to gain access (or just take the whole safe).
My particular situation is uncommon, but the fact remains that no vehicle will ever be secure. They're literally designed with ease of movement as their primary function. If you ask people to leave a weapon in a vehicle, you've just created a parking lot where a relatively large number of the vehicles will have firearms stowed in them.
Alternatively, if one went inside and disarmed at their request, now I'm handling a firearm in a public place. My holster is a Serpa Blackhawk with the paddle attachment - I have three options - drop trou in the middle of the PD's lobby and remove the paddle from my waistband, ask for the nice clerk to stick his or her hands down my pants to hold back the claw on the inside while I do the same for the ones on the outside, or unholster my loaded weapon and hand it to a person whose training is an unknown to me.
Come to think of it... I might go by there and just drop my pants. That's certainly the most amusing option I see here.