Objects that are out of scene/viewport (OpenGL)

Question

Please help me understand what a good way to draw 2D scene (ortho) is. I am using OpenGL with shaders.

If I have a viewport of size 800x600 for example and draw quads. Some quads are in the viewport and some are not.

Are quads that are out of the viewport proccessed by OpenGL and shaders? If yes, do I need to cut them from the draw function? Are there standard decisions (glEnable(???)) for this situation or do I need make one myself?

Draw:

void Draw()
{
  glUseProgram(ProgramId);
  glUniformMatrix4fv(MVPId, 1, GL_FALSE, (float*)pMVP);

  glEnableVertexAttribArray(0);
  glEnableVertexAttribArray(1);
  glEnableVertexAttribArray(2);

  glBindBuffer(GL_ARRAY_BUFFER, BaseQuadBufferId);
  glVertexAttribPointer(0, 2, GL_FLOAT, GL_FALSE, 0, 0);

  glBindBuffer(GL_ARRAY_BUFFER, BaseColorBufferId);
  glVertexAttribPointer(1, 4, GL_FLOAT, GL_FALSE, 0, 0);

  glBindBuffer(GL_ARRAY_BUFFER, OffsetQuadBufferId);
  glVertexAttribPointer(2, 2, GL_FLOAT, GL_FALSE, 0, 0);

  glVertexAttribDivisor(0, 0); //basic size
  glVertexAttribDivisor(1, 0); //basic color
  glVertexAttribDivisor(2, 1); //offset
  glDrawArraysInstanced(GL_QUADS, 0, 4, QuadCount);

  glDisableVertexAttribArray(0);
  glDisableVertexAttribArray(1);
  glDisableVertexAttribArray(2);
}

MVP:

CameraPosition = glm::vec3(0,0,1);
CameraDirection = glm::vec3(0,0,0);
Projection = glm::ortho(0.0f, 800.0f, 0.0f, 600.0f, -1.0f, 1.0f);
Model = glm::mat4(1.0f);
View = glm::lookAt(CameraPosition, CameraDirection, glm::vec3(0,1,0));
MVP = Projection * View * Model;

Vertex Shader:

layout(location = 0) in vec3 vertexPosition;
layout(location = 1) in vec4 vertexColor;
layout(location = 2) in vec2 vertexOffset;

uniform mat4 MVP;
out vec4 Color;

void main()
{
  gl_Position =  MVP * vec4(vertexPosition + vec3(vertexOffset.xy,0), 1);
  Color = vertexColor;
}

Image with question: https://i.sstatic.net/oSiXd.jpg

Answer 1

All vertices submited using glDraw… are processed by the vertex shader (and geometry and/or tesselation shaders if geometry and/or tesselation shaders are used). Only after the vertex processing stage (vertex, tesselation and geometry shaders) clipping can be applied. After clipping only those fragments that fall into the viewport & scissor rectangle and pass the pixel ownership test are being processed.