No, in this case the consumer femtocells on the market (AT&T Cell Booster, Verizon LTE Network Extender) are actual eNodeBs inside the carrier’s RAN. They will IPSEC tunnel back to a security gateway (SeGW), grab provisioning information, and then come up on the carrier’s commercial license as just another (fancy low powered) LTE radio on the network.
AT&T did try to add some additional tamper switches and protection inside their units so they’d brick if you opened them - that was known since the MicroCell era. I believe T-Mobile’s former CellSpots were also tamper-protected in the same manner (they both deployed Nokia LTE small cells).
AT&T also appears to now charge you for the privilege of deploying the newer Cell Booster Pros if you want 5G - I assume that cost ($30/mo per cell!) is basically covering licensing the backend for all of that.
Wi-Fi Calling uses a different SeGW endpoint and is pure IMS back to the carrier voice network, regardless if you shoot it over WiFi or back over a dedicated APN on the LTE network in the normal VoLTE fare.