If you are referring to the populateion of the utag_data object, then the answer is a yes but no.
On every page load, the tealium utag.js script is re-loaded. The properties exposed in utag_data, cannot be persisted via Tealium TiQ (which runs client side).
Now, the 'yes' comes in the form of, you can persist data across page loads using standard methods, such as cookies or browser storage.
However this is not normally recommeded and caution should be taken in determining if this is a solution in your use case.
If you do persist the the values via cookies or storage, note that a client side script (via TiQ) will need to be used (at least for storage certainly) ito pick up the values and pass them to utag.data
hope that helps