Additive genetic variance with $n$ loci
Not in general -- there can be linkage disequilibrium among the loci. For instance, say that there are two di-allelic loci, $A/a$ and $B/b$, and that the frequencies of the $A$ and $B$ alleles are both $1/2$ and that they have the same effect on the trait, with no dominance. If all haplotypes in the population are either $Ab$ or $aB$ (with no $AB$ or $ab$ haplotypes), then the genetic variance at each locus is high, but the total genetic variance for the trait is 0!