Does taking steps to protect my privacy arouse suspicion?

It was on my mind to ask this exact question. With an addition: Do privacy measures arouse suspicion to state security in the processing of visas and monitoring of who comes in and out of borders. I assume at least the US and China do an (automated) online background check for new visa applicants, and I suspect being unable to find data could raise a flag. The flag could be enough to trigger a much more heavy and personalised analysis of the applicant, and could result in a declined application considering how arbitrary these decisions often are.

This seems like such an important question that I too am surprised to have not found it discussed.