Yes! We have taught this to our kids. They have grown up in the faith and have embraced faith in Jesus Christ for their own. They now help to fill the stockings which we hang for everyone waking in our house on Christmas Day. Hanging stockings, having a tree, all the glitter that goes with Christmas adds to the wonder of having God become incarnate as a man and being the Savior of His people.
Yup!
We have St. Nicolas and have always celebrated the saint. It caused a little confusion when they went to school but we just could not allow the secular celebration overtaking the sacred.
I've noticed, too, over time, that because St. Nicholas is emphasized, not the secular Santa, we did not have problems with greedy demands for gifts, or over-the-top expectations of "free" stuff.
This is exactly what I taught, and I have never regretted it. It always felt right. The magic of Santa is preserved (he WAS real, after all), it connects the the seemingly incongruous domains of the sacred and the secular and it resolves that awkward issue of your children someday realizing you lied to them.