It could, depending on the type of misdemeanor and how severe it is. However, it is not a wise idea to be traveling, especially internationally, when you have a pending case as you are usually restricted to intrastate travel until your case is resolved. If the court finds out you're trying to obtain a passport they might consider you more of a flight risk and raise or revoke your bond.
Why bother worry, take care of the warrant, elimint the present and a future issue. It will be no fun re-entering the US to be trans ported directly to detention, and the jail.
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You can probably get the passport, because there is a chance that the warrant will not show up in the application screening process. However, the problem is when you cross the border, both leaving and coming home; there is a chance that the warrant will show up on the Homeland Security Computers. In that situation, they are obligated to take you into custody, and detain you until the agency which issued the warrant comes for you. Potentially, this is much more of a hassle for you than just resolving the warrant at the court which issued it. Contact a good criminal attorney and he will be able to help you with this process.
It doesn't matter. You can and SHOULD just resolve the warrant as soon as possible. If it's a Misdemeanor, it shouldn't be that hard. It's better to resolve it now on your own rather than wait until you're arrested on the warrant.
The question you should really be asking yourself is why haven't you dealt with your Warrent? You really should hire an attorney to help you deal with that Warrent or at least deal with the Warrent yourself. There is no sense in running from the issue. The longer you run the worse it is going to be. Call an attorney today.
Disclaimer: No attorney-client relationship has been established. Please contact an attorney about your legal rights. This answer is for educational purposes only.