Yes it makes sense. It makes even more sense if you then slam a metal pin into the earth and voilà: You have a real earthy-earth.
The point of having ESD straps connected to the Mains Earth is that everything in the world is directly or indirectly connected to the Mains Earth (because it stands on Earth somewhere), so it is the reference point that makes the absolute most sense. But the actual real relevance of the ESD strap is that you are at the exact same level of charge as everything you handle, so that nothing gets zapped and breaks.
So as long as you define a big metal bar or thick wire as "this is my earth here" and connect everything through the methods intended for ESD to that central piece of metal, you will be achieving the exact same thing again.
As said, it is best, for noise effects and such when measuring things, to actually connect it to actual earth by poking a metal pin into the ground somewhere a couple of feet or at least 1m deep, so that the ground you walk on acts as a referenced ground plane and all the earth connections of your devices again react to the environment as they normally would, but if you can't, then the least you can do is connect everything together and call that a safe reference point.
Of course if you are doing that, you do need to keep an eye on: Am I keeping it safe? You must make sure no current can travel from one end of the generator to the other end using your nifty floating (or actual) earth bar, or you might be creating health hazards.
Usually, with most common ESD safe equipment and straps there's a 1Mohm in all the "dangerous" paths that would protect you from harmful currents, but it's better to make sure they can't even happen, than to rely on one single mode of protection.
Best Answer
No, it's not enough to switch off the supply. For most PC's the working voltage has a maximum of 12V, using the Human Body Model (HBM) for Electro Static Discharges (ESD) ranges from 2kV to 8kV, which is hundreds of times more voltage. Whether a circuit is powered on or off will in most cases have very little effect on where the current from an ESD event flows.
The point of preventing ESD is not to 'float' a circuit and remove it from ground (which doesn't happen when a PC is turned off, it should always be grounded when proper electrical codes are followed), it is to stop the charge from accumulating in the first place.
There are transistors (mosfets) that you can destroy simply by waving your hand over them. most of them are older, and many newer electrical components have ESD protection in their inputs, but that gives you an idea of how easy it is to kill electronic parts with static electric fields.
The way to prevent ESD is to strap in, with a 1MΩ resistor on the strap to prevent electrocution. Other ways are, wear an ESD smock, use an ESD mat and to keep humidity high-ish (like 60%) as water vapor increases charge transport through air.
Another thing to keep in mind is that some materials like plastic and paper and clothing readily create\buildup charge so only use ESD compatible materials near sensitive parts.