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I think the difference such an agent makes depends on the starting state. If the DNA was in a double helix that was twisted further this is known as supercoiled) then the agent would cause the supercoiled structure to break down and the DNA to take upa more linear arrangement. This is important because certain circular DNA elements (such as bacterial plasmids) exist in a supercoiled state - imagine an elastic band which is twisted and you'll get the idea. Importantly, DNA in eukaryotic cells is also supercoiled round protein complexes called histones. This allows DNA to be packaged more efficiently.
DNA would break up into individual nucleotides
It depends a lot on the initial conditions, as has mentioned before, but also on the final conditions. If what keeps together nucleotides are removed, the bases might simply exist as pairs. If there is a good deal of energy, then yes, individual nucleotides.