You can be identified quite quickly by other factors if someone with access to data is looking for you. Some factors are writing style networking metadata (who do you contact) and search queries. Especially big data companies (facebook google) are tracking you even if not logged in. Some of these factors are very hard to change from one moment to another, and most people are unaware that this data is used.

The problem with mass surveillance is that even if you are aware you are actively transmitting and your data is still caught in the dragnet for example with camera doorbells and other surveillance apparatus like flock, or visiting a site with facebook ad trackers. You transmit either way by being, if you travel in public with phone or without a phone, both is an identifying datapoint.