It depends how you choose to look at things. If you use the same settings (ISO, aperture and shutter speed), you will get the same image. The metering doesn't affect how the camera creates the image/interprets the sensor details, no -- at least not on current cameras.

But choosing a different metering mode may, in fact, guide you to make different exposure choices when you choose your aperture, shutter speed and ISO, and that will result in a different image. Spot and centre-weighted metering are based on rendering the metered area as a middle grey (18% used to be standard, but it's more varied these days by manufacturer and sensor characteristics). Knowing what's being metered and how you want to render it is up to you. Evaluative metering, at least in more recent cameras, takes readings from enough areas of the picture -- often with colour information included -- to pattern-match against common picture types and come to a more "intelligent" conclusion about exposure. It's not always right, or even nearly right, and it doesn't know what your intentions are, but it is often substantially different from the older, simpler, "dumb" metering options.