Has DNA communication/interaction at a distance been empirically demonstrated?
No — typical DNA extraction will not preserve information about the biochemical state of the cell. 

During the process of DNA extraction, proteins are removed and DNA from a population of cells gets precipitated. Then you dissolve the DNA. In this process native conformational state cannot be preserved. 

However there are techniques (see this post) that can capture long distance molecular interactions of DNA (which reflects a conformational state). To summarize in a line, these techniques "lock" the DNA in its conformation and downstream steps are carefully done so as prevent loss of information.

Stress is just a kind of biochemical response. This technique can be applied to study long range DNA-DNA interactions for different conditions (for e.g. Developmental stages).

Stress can cause RNA in the cell to aggregate; however once you do the extraction you won't be able to know if it was aggregated in the cell before extraction.

An Analogy: Sugar can be anhydrous powder or can be crystalline. But once you dissolve the sugar in water, there is no way to know in what form it existed before dissolution.

Certain processes (epigentic mechanisms) can lead to methylation (sometimes hydroxymethylation) of DNA (at cytosine; Bacteria also have adenine methylation). These modifications can be detected in the extracted DNA by different methods; one of the common techniques employed for this is bisulphite-sequencing. 

Final word: all these claims about molecules having telepathic memory is pseudoscience. There is no evidence whatsoever for such proposed phenomena.