From what I can see, no. I had both a Destiny Knot and Everstone on my Pokemon for both the Tyrunt and Honedge and both Pokemon hatched shiny at opposite sides of the spectrum. If yours is taking awhile just remember, the chance to hatch is the same for each egg.
For those interested, the exact probability of encountering a shiny Pokemon is calculated as follows. The game generates four random numbers ranging from 0 to 65535. These are represented as binary numbers, 16 bits in length. The bitwise operation "exclusive or" is performed on each of the numbers, resulting in a single binary number in the range 0 to 65535. If this number is less than 8, the Pokemon is shiny. Hence the probability of this occuring is 8/65536 or 1/8192.
Pokemon Shiny Gold was released in 2006 after fears that nintendo would not revisit the Jhoto region. It is a hack of Pokemon Fire Red and is a near identical remake of Pokemon Gold, with a few exceptions of course.