I've read about that as a strategy people already employ. My guess is that it doesn't work. There are simply too many dots too easily connected created from using essential technology every day. And too many strong, recurring lines between points. The number of data points used in this manner would far outstrip the fake ones. Since your technological footprint is essentially a profile, I'd further be wary of what sort of fake portrait would emerge of me were I to employ a service that poisons the well with an overabundance of fake data, setting aside the horrible thought of how completely you'd have to give said service access to your services (phone for gps, etc) in order to mask you. That would be a dealbreaker. Then you'd still be stuck with the original problem of the gov't just raiding this company's data stores, even though a lot of it would be fake, -it couldn't help but be tied to your real footprint by at least one node.

It's almost useless. Our online presence leaves information literally everywhere. It's just like DNA left behind every place we habit. The solution won't be a technical one, it has to be a legal, and therefore cultural one. If we don't demand and craft a society that places the utmost value on personal privacy and liberty, then it'll never happen for us, and our Constitutional protection on that issue will fade even further into obscurity. Unfortunately, private free services (especially social ones like Facebook) have trained our population to be ever more comfortable with giving up privacy in exchange for services. When the expectation of privacy is removed from one major area of our lives, it makes it kind of hard to imagine a thriving, resolute, actionable thirst for it elsewhere, -at least to the degree that would motivate action enough to effect political and legal change.

I really wish all the gun nuts were actually privacy nuts, with the same degree of unquenchable, unreasonable passion. It would actually make more sense there. Most of the privacy nuts are barking up the wrong tree imho, with a focus on cryptology and technical solutions.