Yes - its automatically done by machine at the central post office where it is processed (not necessarily where you mailed it).
Remember...you're now into a big mail time (holiday cards). Huge amounts of mail go thru these machines & some go thru together, in which case, the back envelope never gets cancelled & there is no mark indicating when it was mailed.
I'd advise....take it to the post office, wait in line, mail it & ask for a certificate of mailing - it adds 0.90 to a domestic letter & provides you with your own evidence it was mailed on a particular day, no matter what cancellation date appeared on the envelope (or if your envelope got lost after it got to its destination).