No. The Wii U has no SIM card slot, no cellular modem, and no software support for mobile data.
Only Two Ways to Connect Wii U to Internet
Wi-Fi (802.11n 2.4 GHz): Settings → Internet → Connect to Internet → Search for Access Point → Enter password.
Wired Ethernet: Requires Wii LAN Adapter (USB-to-Ethernet, official or compatible). Plug into USB port (back or front). Settings → Internet → Wired Connection.
Workarounds for "No Home Internet"
Phone hotspot: Enable Wi-Fi hotspot on phone → Connect Wii U to that SSID. Uses phone's cellular data. Watch data caps — updates/games are GBs.
Travel router (GL.iNet, etc.): Plug phone via USB tether or insert SIM into router (if router supports modem) → Wii U connects to router's Wi-Fi.
Public Wi-Fi: Library, café, phone carrier hotspot network (e.g., Xfinity, Spectrum). Browser authentication needed (Wii U has basic browser).
What Doesn't Work
USB cellular dongles (no driver support).
SIM in SD card slot (SD slot is for photos/saves only).
Any "3G/4G Wii U" mod — doesn't exist.
Use a phone hotspot or travel router. That's the only path to cellular-backed internet on Wii U.