I have used one of these cheater boxes in the past with relatively good success.
First, if you only have one 20 or one 30 amp outlet available, I would suggest, as Jack does, to use the adapter designed to do this. You really need to have three or four different adapters available to cover all situations.
Regarding the dual adapter, I have found that adjacent 20 and 30 amp outlets at the power pole are generally on different phases of the 240 volt service and you can actually get 240/120 volts. You can pull approximately 50 amps total generally. If there are ground fault protection outlets installed, they will trip and you can not use the cheater box.
Yes, it will work if you can find two outlets that close together. Generally, if the site box only has a one 20 amp and one 30 amp outlet, they are both fed from the same source and probably limited to 30 amps total.† In other words, they are there to give you a choice of connections but not both.
Sometimes you can
steal borrow from an adjacent site if it's vacant but I don't think that adapter would reach.
You can probably make up your own for less money.