Do I also get plasmids in my gDNA extraction?

>> Yes.

Short answer: Yes

Explanation, Spin column (silica column) basically bind DNA, pore size of the column would affect the length of the DNA you get. in case of Plasmid, no matter what you do, if the bacteria had them, plasmid would co-purified with gDNA. except you use magnetic beads with certain ratio to selectively select the length of the DNA you want to isolate (larger than the plasmid)

Yes depending on size of plasmid

The larger the plasmid, the bigger the chance to co-purify it with gDNA. Small plasmids may also appear as contamination. Therefore, it is very likely that your genomic data contains plasmid sequences

It is possible that your genomic DNA also contains plasmid. If you check the prepared gDNA by agarose gel electrophoresis and see low Mol wt. DNA by EtBr staining, you know there is plasmid DNA in the preparation.