Only in certain circumstances. And not always in the way you'd expect. Common sense suggests that introverts will make better lighthouse keepers and extraverts will be better salespeople. This may be true for lighthouse keepers, but one local company found that their successful salespeople were pretty evenly split between introverts and extraverts. So it's important not be lured into overemphasizing personality.
Personality is more likely to be important when work norms are unclear or hard to enforce.
For example, conscientious employees are more likely to exert extra effort when others might decide that enough is enough. Employees higher in integrity are more likely to resist the temptation to pad the expense account, even when they know that they aren't likely to be challenged on a questionable item. Typical employment interviews have a very poor track record for measuring personality accurately. The biggest mistake managers make is using a personality test that doesn't fit the task at hand. Just because everyone is talking about the Meyers-Briggs, the MMPI, or the Caliper doesn't mean that you should use it.