In general, no. People with excellent memories can just as easily misapply the availability heuristic as people with poor memories.
To see why, consider a situation where a reasoner is asked to estimate the relative frequency of murder and suicide. Because examples of murder or more "available" (i.e., more easily recalled) than examples of suicide, the reasoner may conclude that murder is more common than suicide. This conclusion would be mistaken: murder is actually less common than suicide, and murders are only more "available" because they are more likely to be reported in the media than suicides. Note that the problem with this inference is NOT inaccurate memory, but a failure to recognize that memories do not reflect the actual frequencies of murder and suicide.
Of course, someone who has specifically memorized statistics about causes of death -- something that an autistic is perhaps more likely to do -- may be able to draw on that knowledge to answer the question correctly.
For more information on the "suicide paradox," see http://www.freakonomics.com/2011/08/31/new-freakonomics-radio-podcast-the-suicide-paradox/