Not necessarily. Let your baby suck on the first breast (let's call it Breast A) as long as he wants, and then offer Breast B. (Some moms like to take a diaper-change break between, just to make sure baby is good and awake.) If baby goes for Breast B, great. If not, he’s probably full. Begin the next feeding with Breast B.
On the other hand, some babies might accept both breasts, nurse for a while, and still come off hungry. If this happens, just put baby back on Breast A and start over.
In some cases — like when a woman produces an over-supply of milk — it's okay to restrict feedings to one breast at a time, even if baby would accept the other.
Of course, always watch for the number one sign that he's getting enough milk: steady weight gain (after your milk "comes in").