Yes—there can be image differences, but not usually the center-brighter “bloom” effect you’re describing.

A focal-plane shutter exposes different parts of the frame at slightly different times, especially at fast shutter speeds when the shutter forms a moving slit. If a subject is moving quickly, this can cause skew/rolling-shutter-like distortion in addition to normal motion blur. A leaf shutter exposes the frame more nearly all at once, so fast-moving subjects are blurred without that same skew.

Leaf shutters also tend to produce less vibration because there’s no focal-plane curtain strike, which can help reduce shutter shake on some cameras.

As for brightness across the frame: the issue is generally not the center getting longer exposure than the edges. With leaf shutters, any non-instantaneous opening/closing happens near the aperture, so the effect is more like a brief change in effective aperture during the exposure. At wide apertures and very fast shutter speeds, this can sometimes cause slight edge darkening or other subtle aperture-related effects, but it’s usually minor and often invisible in normal use.

So in practice: the main visible difference is motion rendering at high speeds, not luminosity bloom.