It depends though, a secret DVD release of one of these stories would still have to be available publicly for clearance purposes - so they would have to announce it anyway ahead of time.
They would never get a DVD in the shops secretly, because there's no way that retailers wouldn't leak the information that there's (to pick one) "Evil of the Daleks" going on the shelves on such-and-such a date. Long before you reached that point, 2|Entertain would have to produce sales sheets for the buyers at the stores to use so they would know what they're buying and stocking. No retailer is going to stock something blind, especially if they're not even told what it is. In short, way too many people would know, and you couldn't NDA the buyers in every retail establishment in Britain.
About the best the BBC could do would be to announce, a month out, that in a month's time "Evil" will go on sale in a 2-disc set and, that same day, send it for clearance. That's the absolutely best they could do.