You can certainly do this. Render the quad as usual and send the texture to the fragment shader as a sampler2D uniform.
Inside the fragment shader, you can then make calls to either texture or texelFetch. texture samples your texture, and texelFetch looks up an RGB texel from the texture without performing interpolation, etc.
Here is an example of what your fragment shader might look like:
Fragment shader
#version 330 core
uniform vec2 resolution;
uniform sampler2D myTexture;
out vec3 color;
void main()
{
vec2 pos = gl_FragCoord.xy / resolution.xy;
pos.y = resolution.y - pos.y;
color = texture(myTexture, pos).xyz;
}
And then on the application side:
Initialization
glGenTextures(1, &m_textureID);
glBindTexture(GL_TEXTURE_2D, m_textureID);
glTexParameteri(GL_TEXTURE_2D, GL_TEXTURE_MIN_FILTER, GL_LINEAR);
glTexParameteri(GL_TEXTURE_2D, GL_TEXTURE_MAG_FILTER, GL_LINEAR);
glTexImage2D(GL_TEXTURE_2D, 0, GL_RGB, m_imageWidth, m_imageHeight, 0, GL_RGB, GL_UNSIGNED_BYTE, pImage);
m_textureUniformID = glGetUniformLocation(m_programID, "myTexture");
Render loop
glActiveTexture(GL_TEXTURE0);
glBindTexture(GL_TEXTURE_2D, m_textureID);
glUniform1i(m_textureUniformID, 0);