Is bi-allelic gene expression random?

Question

Supposing we have the genotypes “Aa”, “AA”, and “aa”... which are not mono-allelic (not imprinted and not X-inactivated). Does the dominance of the “A” allele over “a” allele affect which gene is transcribed, or are both alleles transcribed and the allelic dominance only determines the observed phenotype? I’m guessing it’s the latter, but that makes me confused as to what the concept of allelic dominance would mean for mono-allelic expression, where only one allele is always expressed and observed.