Don't believe so. She just has those as a normal part of her design (usually just on her drums due to being based off of Raijin's drums visually), but since Chamaji has the whole 'meaningful/punny eye design' thing going on in their art you get this.
It's just a common japanese symbol, called a mitsudomoe. The symbol was already present on her drums in official art. The sharingan also looks distinctly different, albeit similar, so I doubt Raiko here has any specific relation to Naruto outside of using the same extremely common symbol.
