Sort of yes, but indirectly - I've done some work along the lines of experimentation that can do this.
It depends on what you're needs are. If you need USA postal codes, the census web site has zip codes with latitude and longitude data. If you need postal codes for other countries, then I'm not sure where to look other than their post offices.
One way to tackle the problem is to get the codes and get their latitude and longitude coordinates. From this, you can use this info to match up the postal code the user has entered in. Then with the user's lat/long, you can compare it against the lat/long values you have in your database and with some math, calculate a distance. Just a week or so ago a friend of mine hooked me up with a MySQL C function that does the math and calculates the distance between two coordinates. You'd need root access to MySQL to install it so let me know if you need it.
