Visual perception persists in the absence of functional eye movement.
An example case would be retinal implants wearers. Retinal implants like the Argus II consist of a set of electrodes placed onto the degenerate retina of blind folks. Electrical stimulation of the electrode array elicits flashes of light (phosphenes). Visual input is provided via a head-mounted camera, and the device translates the camera images into patterned electrode stimuli. Hence, because the camera is head worn, Argus II wearers cannot use eye movements to scan the world. They have to use head-scanning techniques. Still they are able to perceive flashes of light (phosphenes) and can recognize simple shapes and perceive motion.
In fact, eye movements such as saccades are detrimental in Argus II wearers, because the oculomotor system feedbacks muscle movements to the brain when a saccade is made to stabilize the perceptual field of view. In normally sighted people the oculomotor feedback system is important, as it tells the brain to compensate the retinal image position shift when a saccade is made. Compensation occurs through a shift in the brain representation of the retinal image to the opposite direction, thereby stabilizing the image representation. However, this is detrimental in Argus II wearers, because the position of the electrode array and hence retinal position of the image is unaffected by eye position. Hence, when subjects use their implant, any saccades will disrupt visual processing, because the oculomotor system will abberantly compensate the perceived location of the object being viewed.
More importantly, perhaps, are micro-saccades. Micro- saccades are small, involuntary eye movements. When images are present stably to the retina the images fade very quickly due to adaptive processes in retinal neurons. Micro-saccades are thought to prevent fading, as they constantly produce small, involuntary fluctuations in gaze, thereby shifting the image quickly over the retina, and thereby refreshing the retinal image and preventing adaptation (Stingl, 2013). When Argus II wearers stop scanning the image, images indeed fade within seconds (Stronks, 2013).
To get back to your question and summarize:
Title question: No, eye muscles are not needed for sight, given that Argus II wearers have sight (though artificial, crude vision). However, a functional saccade system in normally sighted folks improves scanning, and anecdotally micro-saccades prevent image fading by constantly refreshing the retinal image.
Body question: Argus II implant wearers are an example of vision without oculomotor control. Although they cannot use their eye muscles for scanning, they still have functional vision.
However image fading is a problem in Argus II users and folks without functional eye muscles alike, so head scanning techniques will be needed.
PS: Other implant systems, such as the Alpha-IMS use light-capturing methods inside the eye. Hence these subjects can use normal eye scanning and saccades for scanning. Also, albeit anecdotally, fading is reduced in Alpha-IMS wearers, because of the micro-saccades preventing adaptation (Stingl, 2013).
- Stingl et al., Proc Royal Soc B (2013); 280(1757)
- Stronks et al., IOVS (2013); 54(6): 3891–901.