Yes, a child might attribute any social non-acceptance in the classroom to being a different age, if age is the largest difference which they perceive. For example, a child might not accurately observe or articulate the differences between their responses and the responses of other children... or they might erroneously attribute the differences in responses, to their age difference. Some adults may do this as well... labeling any social difficulties as "immaturity," when other factors may be at play.

The classroom teacher's knowledge about acceleration (grade-skipping) can go a long way toward creating a positive classroom atmosphere for an accelerated student. Taking the emphasis off of age and re-framing the child's placement as a matter of where the child needs to be can be very effective. Instead of highlighting a difference between children, this emphasizes something which the children have in common. An example of this: Tamara Fisher's blog post The Right Fit, linked in this old post.