Statistical tests for PRNG that generates a sequence which is not binary
Randomness testing uses asymptotic properties. Thus, as the length of your input increases the effect you are concerned about will disappear. 

Specifically, there is no need to convert ternary $1$ or $2-$tuples to binary. If you let $n$ increase you cover the interval $\{0,1,\ldots,3^n-1\}$ and then you convert these integers to binary, paying at most a 1 trit (Shannon's term for entropy in base 3) penalty in entropy. Since a decent ternary source should yield not much less than $$\left(\frac{\log 3}{\log 2}\right)n$$ bits or $n$ trits of entropy, there is nothing to worry about.