My understanding of the scene modes is they affect exposure only. They will choose what the camera decides is an appropriate combo of aperture and shutter speed, weighted toward the type of scene selected.
You can adjust exposure post processing, although there are limits. I normally consider I can make up to 3 stops adjustments to an image. Beyond that you begin to loose detail. For most scenes, I doubt you will see a significantly different total exposure between different camera settings, excepting manual.
The things that it will be difficult to manipulate post processing are shutter speed and depth of field consequences. If you are using too low a shutter speed, depending on camera steadiness and subject movement, you will experience blur that will be difficult to impossible to do much about after the fact. Of course, sometimes you actually want subject, or background blur to convey a sense of motion.
With depth of field, again, recovering detail from blurry sections of the image that are outside the depth of field from a large aperture, is difficult. There are some AI programs available these days that can ameliorate that blur to a degree, but that is more of a rescue operation that should be avoided if possible IMO. There is a sharpness adjustment in most all post processing software that will increase sharpness, but again it only helps a little, it won't bring a badly out of focus image into sharp detail. Often a shallow depth of field is desirable. Portraits, and a lot of wildlife photography will frequently benefit from a nicely blurred background contrasted with a crisp subject. This can be obtained by use of longer focal lengths, or wide open apertures.
This picture has a nicely blurred background that I believe adds to the feel of the image. It was shot at nearly wide open aperture, using a long focal length lens. There would be no way to sharpen the background to any appreciable degree post processing. A smaller F stop would bring more detail to the background, although at 500mm and the distance between the subject and the background, you would not be able to get it sharp. Of course, I would not want it sharp.
My advice, would be to ditch the program modes, and use either aperture preferred, shutter speed preferred, or manual. You will need to make a decision before shooting of what you want from the image and choose a setting that will give you that. I normally shoot in aperture mode. I keep an eye on the shutter speeds the camera is giving me, and will occasionally tweak the aperture, or overide the exposure by a stop or two when necessary. This will give you much more control over your images.
On a side note, after switching to RAW, I noticed my pictures straight from the camera were often drab compared to the JPEG images. However, all the vividness, and detail was available with just a little bit of post processing. I believe I have more options and control post processing RAW images vs JPEGs.