Yes - and No.
Yes, you can develop a very large program purely in binary - it's how we started in this game and the first operating systems and everything else were written that way.
But...it's slow. Very slow. That's why one of the first things written in binary was a basic assembler, to translate "readable" machine code instructions
LD A,(HL)
into the binary equivalent teh processor understood:
01111110
This was a lot quicker! But...still a lot slower than modern languages - it takes 1/10th the time to code in assembler than it does in binary, but 1/100th the time to code in C# than assembler.
So any "large project" you try to code in binary is going to take a significant amount of time.
The "and No" part is that it won't run on "any operation system" anyway, an executable program for Windows won't work on Android, even if it running on the same hardware.
And that leads us to the really big one: different hardware interprets binary values differently, so what works on your PC processor won't work on a first generation PC, or on an iPhone, or a Tablet, or...
So the real answer is "No". this won't work, and even if you restrict yourself to a single defined platform it's not really a practical idea!