You can do that - well sort of. You have to draw one rectangle (lets say this is rect1), set this rectangle stroke style and and paint color to "unset paint" - little question mark button on Fill and Stroke dialog. Then you make CLONE of this button lets say clone1 which is quare, select rect1 again and make another clone clone2 whis you can set to be a rectangle.
So you have: rect1 - square, clone1 - also square and clone 2 - rectangle
you can then make all square and rectangle buttons with clones of those two clones - add shadow, round the corners, make inner signs or you can copy it from gray buttons. The two original clones copy color from the parent, and the child clones (your buttons) copies it from their parent also - from the first two clones.
But when you change original square (rect1) color it changes colors for each rectangle/quare at the same time.
Mission possible

Is that what you want???
I got the idea from Nicu's howto -
http://howto.nicubunu.ro/webcomic-cartoon-title-inkscape/Sorry about my "bad" grammar, english isn't my first language.