That's really a trick question; but you wouldn't know it by just thinking about it in passing. Well, I guess you could say it's a trick answer... anyway...
Assuming you just chapped the background out of the original photo:
If you measured the colors with Photoshop's built in colorimeter, they would read the same as they did before you chopped the background out.
If you actually look with your eyes at the colors before and after, they may have changed or not. It would depend upon the new background color and the proportion of the foreground and background image areas. It's most likely that they would change and possibly quite drastically.
The human eye sees nothing "in a vacuum." Everything that the eye sees is related to what else is seen. The perception of color is directly related to what colors are surrounding, contained within, or in the general vicinity of the "target" color.
Go look at your wall. Since they are usually painted a nice solid color over large areas, your eyes will begin to adjust and perceive more detail the longer you look at it. This is because the eye adjusts to current conditions. If you throw up a strongly colored piece of paper or other object next to the wall so that it takes up a sizeable portion of your viewing area, the detail that was once perceived in the wall will diminish until there is an new equilibrium of perceived detail between the wall and the new object.
Basically, human color perception is dependent upon what surrounds the "target" color and the viewing conditions.
You pretty much have your choice between the two models of color measurement to choose from: The colorimeter version where a piece of equipment or software tells you the reflected RGB values of the color or the one where you believe your own eyes.
I know which one I choose.
(Sorry if I answered the wrong question or went of on a tangent. I do that sometimes.)