Yes, this can be possible, although Inkscape may not be the optimal tool for it. What you probably want for a job like this is a raster graphics editor like GIMP or Photoshop, not a vector graphics editor like Inkscape.

Without seeing the actual picture, though, it's hard to say just what could be done with it and how. Still, just to show what is possible, here's a picture I once cleaned up for Wikipedia using GIMP:

The original is on the left, the edited version on the right. Of course, neither version has particularly high resolution, but the result still worked fine for its intended use, which was as a tiny 30 × 20 px thumbnail in a boilerplate notice. (Since then, I've seen that same mouse show up in some surprising places, which just goes to show that there's always demand for simple public domain clip art, even of lab mice.)

Edit: OK, after looking at the original image, it seems to me that this is mostly a white balance issue. Assuming that the wall behind the subject is actually supposed to be gray, we can easily fix the issue using the GIMP white balance plugin:

1. Use the Color Picker Tool to select the color of the wall as the foreground color. (Since we have a nice flat expanse of wall to select from, I suggets using "Sample average" and a fairly large radius for best results.)

2. Use the white balance tool (Filters → Colors → White balance) in "Make foreground gray" mode.

(You can also do this just by playing with the sliders in Colors → Color Balance..., but the plugin makes it a lot easier.)

These steps will correct the color cast, but the resulting image is still kind of dark and grayish. So the next step is to brighten it using the Colors → Levels... (or Curves..., which is more versatile but also more complex) tool. This will take some trial and error to get the best results, but basically you first set the black and white points so that the histogram just fits between them, and then adjust the midpoint slider (or a control point in the middle, if using curves) to get a nice contrast. This is what I got after playing with curves a bit:

If the result still looks too "bland" or gray, you might also want to push up the color saturation a little (using Colors → Hue-Saturation...). Be careful, though, it's easy to overdo it.

Ps. You'll notice that the wall in the background still loks gray, not white. If you really wanted it to be white, you'd basically have to cut out the subject and replace the background, which is a lot more laborious than simple color balance adjustment. (If you just try to push up the brightness until the background becomes white, you'll notice that the highlights on the subject also burn out completely.) If a light gray background is not sufficient for you, it might actually be easier to take a new set of pictures with better lighting.