Yes, jade can sometimes appear in a color that could be considered pink. However, this coloration is more accurately described as lavender in the gem trade.
While jadeite, one of the two minerals properly called jade, is available in a wide range of colors, true pink is rare. The "pink" jade typically seen is more of a light purple or lavender hue. Guatemalan jadeite, though rare, also boasts blue examples.
In summary, while not traditionally thought of as a common color for jade, pinkish or lavender shades do exist, particularly in jadeite.