FBO Attached Textures Reused as Shader Source Textures

I have a GLSL Shader that renders to multiple GL_LUMINANCE textures in an FBO. After the FBO render is complete, I then use these same target textures as source texture Samplers in a different shader.

My question is:

Do I need to unattach these textures from the FBO before I can use them as source textures in another shader?

No, you do not need to.

Thanks very much.