Yes, that is exactly how I was trained by my mother to always acknowledge any gift. I don’t think many kids get that kind of instruction anymore. I always call to thank people for sending a card, no gift inside needed. I think it is nice that someone takes the time to send a birthday card. Many times over the last few years, my husband and I go to a wedding, give 50 or 100 in cash and don’t hear from the bride and groom for so many months, you wonder if the card got stolen. Eventually, we do get a card, but after 4 to 6 months, the thank you is rather hollow.
I married into an Italian family, everything was written down, so that when it was our turn to give we knew how much to give. lol, it was a good system and kept everyone happy. Thank you cards were send within two weeks max.