It's possible, but I don't think it's likely. D-notices are very British things - they're a polite request to the media not to report on specific areas, and carry no legal weight. The assumption is that as long as they are issued in good faith, then the media goes along with them and everyone's happy because the security services don't have to start lobbying for censorship powers.
Now, along comes a situation which looks a lot like an attempt at journalistic suppression by the state. The incentive for the media to go along with any potential D-notice has evaporated because this is just censorship by other means, and if you're going to censor us anyway, why bother with D-notices? Issuing a D-notice over harrassing a journalist (via their family, in this case) would be something of a bodyliner, and I don't think even the British press would have a hard time figuring out what to do about it.
The super-injunctions were ridiculed pretty much out of existence. TV newscasters talked so much about them they started letting names slip or details sufficient that "everyone" knew. Twitter was overflowing of people publishing the names. TV comedians ridiculed anyone involved, and made jokes about how they'd get arrested, faked calls from their lawyers to shows they were on, and in general showed no respect for them.
If anyone issued a super-injunction over this, the British media would see it as a challenge as to who could ensure the details were insinuated in such as way as to ensure the widest distribution.
