It likely will, as blue+pink would equal purple. Can vouch for this as I had some remnants of Arctic Fox Virgin Pink and put Arctic Fox Aquamarine over it. The places that the pink clung on to more became a muted purple. Fortunately it was just on a few pieces more towards the ends. It blended really nicely, but depending on how much of your hair is currently pink, it should be some form of purple. I bet it'll be really pretty though! Post pics!
Strand test of the blue on a very small section is strongly suggested. Opinion will result in some shade of purple.
I put a super dark blue over very faded pink and it was blue, but my pink was super faded and the blie was almost black it was so dark. Rockabilly blue is a pretty strong color, strand test it. If it comes out purple I would suggest fading out your pink more.
"If you don't know where you're going, any road will get you there." <---Lewis Carrol