Very unlikely. DNA and RNA share many of their physical and chemical properties, so they cannot be distinguished without specific enzymatic activity. RNA is more liable to heating, though, but required thermal treatment will most probably not leave DNA intact.

For a quick DNA extraction for PCR we tend to use:

Article Fast and Reliable PCR Amplification from Aspergillus fumigat...

However, if you want to remove RNA for downstream processing you could try a DNA purification column, or run a agarose gel and do a gel extraction?

Simple answer, NO! You would need RNase treatment.

No, you have to treat with RNase.

no, you definitely have to use RNase to remove the contamination by RNA in your DNA sample

Thanks everyone for the answers and replies, I'll try to modify my methods.