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In theory you can use Inkscape, but practically you'll most likely have more work getting your stuff to look good later, even if it's just due to reducing the number of colors (Inkscape will use aliasing after all).

Draw a simple character or object, export it as a 16x16 pixel image (Gameboy games typically used 8x8 or 16x16 for tiles and sprites) and see how it looks like and how much work it is for you to get it right (i.e. reduce it to 4 colors or 1 transparent + 3 colors while still looking good)