There's only one exposure level (ie: amount of light) per picture; spot metering just means that the "target" level is based off of a particular area rather than the average of the whole frame (or some fancier means such as matrix).
Another means of setting the exposure level is through your manual controls (shutter, aperture, ISO). If you're changing your shutter and getting a new (non-washed-out) exposure level, then it sounds like this is what you're actually doing -- not spot metering. (If you were changing your shutter and still getting a similar exposure, then you'd probably be in aperture priority mode, and the camera would be compensating; this could still be using spot metering.) Note that you can base your exposure off the results of a spot meter, but the minute you change your dials you're effectively in manual mode.
You can change your effective exposure in post-processing, and get similar results as changing it in-camera. Of course, the results may not be exactly the same: shutter speed will change your blur; aperture will change your depth of field, ISO will change your noise, post-processing could introduce all sorts of artifacts.
The nice thing about post-processing programs is that they will let you selectively adjust exposure. You could change just part of your image area, or you could change the contrast, or change the brightness of one particular color. And, of course, you could undo and redo your changes without taking a new picture.
Lastly: note that if you overexpose your shot in-camera too much, you'll "blow out" the brighter part of your exposure and lose detail. This is difficult-to-impossible to fix in post production. It's also particularly a problem with digital imaging; film works differently in this respect. Most higher-end digicams will have a "blinking highlight" function that will show you when & where you've done this.