A working model flying sub is definitely possible, especially with modern electric power with lipo and brushless motors. I do a bit of model flying, so I'm clued up on wing loadings. It probably wouldn't be a very nice aeroplane to fly, and a rather indifferent submarine, so I'm happy to hand that particular challenge onto someone else.
Used to race off-road 1/10th scale cars when I was younger, but it got too exotic and costs spiralled. As a schoolkid, I couldn't keep up with well heeled adults, so I went back to marine stuff where ingenuity counted for more than the size of a wallet.