Penalty for Non-State-Changing Texture Rebinding in OpenGL

Changing active textures is an expensive operation in OpenGL. I am in the process of optimizing some code by batching drawn objects by their needed textures. I have already implemented a fix for this problem on the application side but I am wanting an answer to a question that popped up while I did so.

Say I have the following code:

bindTexture(tex1);
draw();

changeSomeUniforms();
bindTexture(tex1);    // I rebind the same texture as used above! 
draw();

bindTexture(tex2);
draw();

Assuming all textures are getting bound to GL_TEXTURE0, is OpenGL capable of ignoring the unnecessary rebind of tex1 without my intervention? Since the call does not change the state of OpenGL, does OpenGL ignore it?

I currently batch things by similar texture so the above is in my application like so:

bindTexture(tex1);
draw();

changeSomeUniforms();
draw();

bindTexture(tex2);
draw();

I wanted to know if OpenGL was smarter than me and did not rebind the same texture without my intervention?