If your genomic DNA (gDNA) extract includes native plasmid DNA, it is likely that you will receive sequencing reads for those plasmids. Generally, DNA fragments with a size of <1 kb are excluded during sequencing. However, small plasmid-sized reads are not filtered out during assembly, so there is a probability that they will contribute to their own plasmid assemblies in addition to the gDNA assembly.
Ultimately, the types of DNA in your sample that contribute to an assembly will depend on the overall sample quality, coverage, and the relative abundance or degradation of each type of DNA.