I'm Danish and I can confirm that this is almost correct. The normal definitive form is "vandet".
However, there is a special case: when you order a bottle of soda water in a restaurant, then you say "en vand, tak". It simply means an unspecified soda, so you'll probably be asked if you want a coke, orange, or so. I've never heard anybody say "her er vanden" ("here is the water"), I believe it's only used as "en vand".