Besides 3D movies, have you used some type of 3D display? Whether you noticed it or not, there are actually two types of focusing going on a the same time.
I'll call the first type "stereoscopic depth". The disparity between the two images that each eye sees is what gives the 3D illusion, as your eyes try and focus to different depths in order to fuse the two images. You can visualize this, as mentioned below, by holding your finger at arms length and switching between that and your monitor. You should see two blurry fingers when you look at your monitor.
The second type I will call "image depth". This is the focusing of the lens of your eye to get a sharp image projected on to your retina. You can visualize this with an outstretched finger, but this time close one eye. With the open eye switch between your finger and monitor and notice how your finger is still blurry when focused on your monitor, but much more subtly. This actually hinders most stereoscopic displays, because your brain has trouble compensating for the fact that when it focuses on the "stereoscopic depth" it is getting the wrong "image depth".
In 3D movies, you don't notice it so much because the focal plane is already so far away, however for TVs or computer screens, or even head mounted devices, the effect is much more pronounced. It is also one of the contributing factors to sickness and headaches while using VR environments.
So while you say that your eyes will always be focused on the computer screen, you actually have it backwards. Your eyes will be trying to focus on the perceived 3D depth. And therefore, you will not be able to perceive both near and far objects as being in focus at the same time, just like in real life, and jumping between them rapidly could cause more of a problem than in real life because you are missing the 2nd focus queue of proper "image depth".