TLDR: The thrust would not double. You can get close but it won't be easy.
There are a lot of factors affecting this but in my experience the distance between props dominates.
I once built a push-pull RC airplane and got close to 180% the thrust of a single prop. The configuration is similar to the Dornier Do335:
So you can get quite close to double. But look at the distance between the props. That's at least 5 times prop width.
I've also tried building a coaxial two motor EDF unit. The result was I got at best around 106% thrust - that's right, the second motor takes twice the power but only adds 6% of additional thrust.
I've also tried coaxial configurations outside of a ducted system and got around 120% thrust. So a second motor takes twice the power but added 20% thrust. This was OK because at the time I was depending on the coaxial rotation to counter torque.
But this is all anecdotal from my personal experience. So I wanted to find any research on this and it turns out that someone at Rutgers University have already done the experiments: https://rucore.libraries.rutgers.edu/rutgers-lib/55491/
I'll quote the relevant conclusions:
With a pitch of 4.4 inches, contrarotating second, third, and fourth rotors
roduced 71%, 53%, and 41% of the first rotor’s thrust, respectively. With a pitch of 4.4 inches, co-rotating second, third, and fourth rotors produced 61%, 42%, and 40% of the first rotor’s thrust, respectively. This confirmed that contra-rotating coaxial rotors generate more thrust than co-rotating coaxial rotors by effectively recovering the energy put into the swirl of the leading propeller’s wake. With a pitch of 10 inches, co-rotating second, third, and fourth rotors produced 97%, 67%, and 54% of the first rotor’s thrust, respectively. This demonstrated that downstream propellers are capable of generating more thrust when operating at higher pitches. The thrust losses of the downstream propellers do not have to be as high as they typically are.
Note that they managed to get almost double the thrust of a single propeller: 197%. But for this to work the second propeller had to have a much higher pitch than the first.
But do note that in the section of the report about thrust measurements (page 46) the author cautiously noted:
Although a multirotor system could benefit greatly from a coaxial arrangements, some can be an exercise in futility.
If you really want to know if your idea would work I'd suggest building a test jig and measure the thrust. Use the Rutgers paper as a guide for how to tweak the configuration (eg: making the second prop have higher pitch)