Yes,

If you are using a spectrometer method you'll need to calibrate the reading with high grade water. 

If you you do not you'll get reading of various containment as a result of absorption. It may be able to tell you how much DNA you have but will not give a clear indication of quality.  

If you don't use nuclease free water you risk your dna to be attacked by DNases. This will affect your DNA yeild and might degrade your DNA.

Best, 

Hamadi

It depends on what you need the DNA for. For routine techniques, this probably won't matter at all (assuming you (dilute with sterile water? and) quantitate the DNA reasonably quickly. But if you need precise quantification, then every step of your procedure should be done using best practice. Best practice for DNA preparation is to use nuclease-free everything (reagents, tubes, etc.).

The repercussion could be that your DNA becomes somewhat degraded and your concentration is off (of course, that depends on how you are quantitating)...and so your concentration isn't quite right and that DNA is a bit chopped up, although the DNA back in the prep tube is just fine (assuming you've used nuclease-free reagents, etc. to prepare that).

Are you asking for a specific reason or for the 'theoretical' answer?