Collisions are independent of drawing.

A collision will not happen if the instances involved in the collision do not have a sprite_index assigned or a mask_index assigned (I'm pretty sure you can have a mask with no sprite, which would just be an invisible wall). If you are just drawing sprites, then there can be no collision as sprite_index hadn't been assigned, if that's what you're asking.


And to put it the other way around, collisions can happen even if you skip draw. As long as an instance has a collision mask, which it by default inherits from attached sprite, it is capable of generating collisions. In contrast, whatever you do in draw won't have any bearing on anything. It is just a visual. Although, many times you will be drawing the attached sprite because that's what you have intended the instance to represent.


If you are wanting to use image_angle to rotate, this will change the size of the mask if it is set to rectangular. Instead, you can use a variable, such as my_angle, where you store the rotation, and then just draw that variable as the image_angle argument using draw_sprite_ext().
An example of this is shown here.