Does this mean I can pack an adgroup with hundreds of website-relative keywords and insert {keyword:} into the heading and my ad will be relevant to all keywords?
Yes this is possible, I do it all the time, but you must ensure your text ads are relevant and make sense when doing so. I usually do not utilize KDI in the long run but its a great way to get things started to see which keywords I should focus on. Then create 1 to 1 adgroups and write even better and more targeted text ads for your volume drivers
DKI is a good tool to write ads for a large volume, but as Robert said make sure that your ads make sense for each keyword in your ad group. There are a couple of things to watch out for. One is that the keyword that triggers your ad may not be appropriate to your ad, it's just enough to trigger your ad and then inserts a phrase which doesn't make sense. You do often see this in Ebay ads (just see the Funny Adwords Ads post for a few laughs). Eg. I saw a baby products ad that was bidding on the word nappies, when someone searched for dirty nappies it inserted that phrase into the ad text. Also, be aware that other advertisers also use DKI so you can end up with a few ad titles the same on the results page. If you can add any text before/after the keyword variable, you'll distinguish your ad from the competition better. Eg. Get {keyword:default text}