Or should the user have complete control? The intention is to have a slider/carousel that shows 6 or 7 images which the user can look through by clicking arrow buttons left or right. But the question has also come up if the user has not started looking through the images, should the carousel start automatically rotating the images. Since this is for a mobile site, I'm uncertain...
I don't have a definitive answer to your question, but there are two things to keep in mind: user control of the carousel's rotation and mobile-specific gotchas.
The Web Content Accessibility Guidlines (WCAG 2.0) are quite clear: users must have control over timed content:
For any auto-updating information that (1) starts automatically and (2) is presented in parallel with other content, there is a mechanism for the user to pause, stop, or hide it or to control the frequency of the update unless the auto-updating is part of an activity where it is essential.
If you do choose to automatically start carousel rotation, then, definitely provide means to pause the rotation.
I can think of one case where an automatically playing carousel on a mobile site may present more problems than its desktop equivalent. Consider a carousel placed on a particularly long page. Unless specifically set to render the page at a different zoom level, the mobile browser will show the page zoomed all the way out (displaying the full length of the page), likely making the carousel content unreadably small. In order to read the carousel, the user would have to zoom in. The carousel's automatically advancing to the next frame while zooming could result in some user frustration.
So, as long as the user maintains some control over the carousel's rotation and as long as mobile-specific interactions won't make the carousel harder to use, automatically cycling the carousel is probably acceptable. But, as Rahul pointed out in his comment, just because a carousel is acceptable doesn't mean that it's effective.
Why not give the option of pausing the slider on action? If the intent is to go and display all the slides, it would probably be wise to have it set to automatically rotate through the slides, and upon the users action of clicking on the arrows, the slider could pause since they were trying to go back and read/look at one of the slides more clearly.
I don't see the difference in functionality whether it be mobile or desktop.