Hypothetical, imagine your fake profile indicates you are a minority in some demographic dimension that is now out of favor politically. The dragnet would not really care if it happens to be true for you or not.
I'm recalling the Turkish cleansing of a local religious sect from all government jobs when its two leaders had a falling-out. This could happen in any country, imo.
If there is a conflict and you don't know who will come out on top, either support both of them (one actual support and one fake) or don't support either of them.
Either way, I believe that this topic of giving incorrect information is worth looking more into.
Even if Google/NSA knows your name, they can only see the online activity that you choose to do. You can intentionally choose to give them very incorrect online activity.
For example, intentionally visit websites (manually or automated) that you don't believe it. This will trip up their algorithm. How are they supposed to know what you actually think or believe in?
Imo the claim "We can suggest what you should do next, what you care about. Imagine: We know where you are, we know what you like." is just a sales pitch to the data industry in disguise.
They know what we do, but it isn't possible to know what we think without making a bunch of assumptions
Avoiding surveillance is becoming very hard. But giving incorrect information is very easy.