No. I suspect this defense is probably not a great use of your time.
If you didn't have the links, the information would be hard for you to use -- hard for the good guys to use easily. That's bad for usability, because is information isn't easy to use, it probably isn't of much use to many of your users. But the bad guys aren't under those constraints. The bad guys could probably still gain a lot of sensitive information, and piece things together enough to give you a bad day.
Do you remember the story of Iranian revolutionary students who stormed the US embassy in Iran? The US residents shredded many of their documents before evacuating, but the Iranian students were still able to meticulously piece together the fragments of shredded documents into a whole, like a jigsaw puzzle. They had the time and patience to do it. Those shredded documents would have been pretty much useless to a legitimate authorized US diplomat, but they were enough for the attackers to work out a lot of sensitive information the US didn't want them to have. Security is often like that; the bad guys are willing to put in more effort to recover your data than any ordinary user of your site would be.
And in any case, if your site gets hacked, do you want to be in a position to tell the press "Oh, yeah, they got all the data, but they didn't get the links, so it's all good?" That doesn't sound like the kind of thing that is going to inspire trust among your customers. It's not a pretty picture.
So, I suggest you spend your energy elsewhere. Remember, security is a risk management effort. That means you need to prioritize where you spend your time, based upon what gives you the most security benefit for the least time, energy, and cost. I don't think this defense is a good one. Instead, I'd focus on the basics, things like application security (SDL), configuration management, network security, disaster preparation and recovery, internal education, and so forth. Most organizations have a lot of room to improve, even on the basics.