I'd like to give you a straight yes or no answer, but it all comes down to the offset of the DX wheels. They'll fit on, but far as I know, the offset on stock 13" 6th Gen wheels is around 38p, whereas the stock offset on 14" 7th Gen wheels is around 42p. So in that instance, the 6th Gen DX wheels would sit 4mm further from the wheel well/suspension components. If you haven't lowered the car then it shouldn't rub or cause any issues, but if your car is lower than factory height then you may find that you have to roll your rear fenders.
As for the speedometer, it will only be inaccurate by 1mph. So when it reads 70mph, you'll actually be doing 71mph.
With a bit of luck, the offset will be stamped on the inside of the wheel. If not, then the easiest way to measure it is with the wheel lying flat on the ground. What you do is measure the overall width of the wheel then divide that figure by two. This will give you the centerline of the wheel. After you've determined the centerline, measure from the hubface to the edge of the wheel (where the tire mounts to the rim). Subtract the centerline figure from that measurement and the remainder will be your offset.
There are plenty of online calculators that allow you to enter the offset of your standard wheels as well as the offset of the wheels you are wanting to put on, which will tell you how much clearance you'll have within the guard. However this is a site that I swear by:
http://www.carbibles.com/tyre_bible_pg4.html
There's a good chance that they will fit like a glove and won't cause you any issues at all, but it pays to check these things before purchasing different wheels. Hopefully someone will come into this thread who has used stock 6th Gen wheels on their 7th Gen before and be able to put your mind at ease. Best of luck