Can I pellet DNA back from dissolved state?
No, you cannot pellet dissolved DNA with ultracentrifugation.

Yes, you can recover a pellet with additional treatments, similarly to how you got it in the first place; only instead of your input being homogenized cells, or tissue, or extract, or whatever you used to obtain your DNA, it would now just be your aqueous solution of DNA.

For instance, you may have performed a TRIzol extraction to separate your DNA into an aqueous phase, prior to spinning it through mini prep columns to elute your purified DNA in water. You could perform the procedure again and you'd have your pellet once more after the final alcohol (ethanol or isopropanol) precipitation step.

The key idea with pelleting DNA (or any nucleic acid) is to make it insoluble; this is achieved with by using alcohols and salts. If it is soluble, nucleic acids cannot 'come out of solution' to form a pellet.