If the frequency of one of the alleles is close to zero when the simulation starts, if there is no selection, is it likely to persist?

NO, if the frequency is low the alleles is not persisting according to the rule of natural selection.

Explanation:

Directional selection leads to increase over time in the frequency of a favored allele. Among alleles dominance relationship advantageous rate gets fixed. The reason behind it is rare alleles are mostly found in heterozygotes.

By natural selection when it reaches high frequency then recessive mutation can be seen. After reaching on advantageous allele reached at high frequency that time deleterious alleles are very necessarily rare and due to this it is mostly present in heterozygotes