Does race condition produce biased pseudo random numbers?

When trying to make a legacy library reproducible (set a certain seed and you'll always get the same result), I discovered a race condition bug which looks like this

#ifndef _OPENMP
#error "OpenMP support is required for this MCVE"
#endif

#include <Rcpp.h>
#include <random>
#include <omp.h>

using namespace std;
using namespace Rcpp;

// [[Rcpp::plugins(openmp)]]
// [[Rcpp::export]]
NumericVector random_vec(int length, int n_cores) {
    /* 
     *  Returns a random vector of LENGTH.
     */
    NumericVector result(length);

    // Set up seed for each thread
    IntegerVector seeds(n_cores);
    seeds = INT_MAX * runif(n_cores);

    // !!!RACE CONDITION!!!
    int elem1, elem2;

    omp_set_num_threads(n_cores);

#pragma omp parallel shared(result)
    {
        // Seed each thread with a deterministic seed
        mt19937_64 mt(seeds[omp_get_thread_num()]);

        // I'm aware that WRE discourses the use of <random>, but I'm
        // maintaining a legacy codebase and I don't want to change
        // the existing code unless there is some drop-in replacement.
        uniform_int_distribution<> r_unif(INT_MIN / 2, INT_MAX / 2);

#pragma omp for schedule(static) nowait
        for (int i = 0; i < length; i++) {
            // Threads overwrite the values set by each other
            elem1 = r_unif(mt);
            elem2 = r_unif(mt);

            result[i] = elem1 + elem2;
        }
    }

    return result;
}

While it has been fixed, the library have been used for various research projects, so I want to estimate the impact of this bug. A few simulations indicates that the distribution of random numbers generated don't change significantly with or without a race condition, but is there a case where it actually makes a difference?