Set up and use a Wii U without a separate display

You require the physical Wii and an SD card to move everything over. Note that this is a "move", not a "copy"; everything that gets put on the Wii U will be deleted from the Wii.

Important! You will need to have both the Wii U and Wii on hand to perform a system transfer.

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3. If I transfer my games from Wii to Wii U, can I keep the games on both hardware?

• Once the games are transferred from Wii to Wii U, the games are no longer usable on the Wii hardware.

4. I forgot to transfer my digital games before I traded in my hardware, can I get these games back?

• Once the console is traded, we have no way to retrieve the data.

5. What Data is Transferred During a Wii to Wii U System Transfer, and what data is not Transferred?

The following is transferred during the system transfer process between a Wii and Wii U:

• Wii Software Save Data
• WiiWare and Save Data
• Virtual Console titles and Save Data

Source: http://www.nintendo.com/consumer/systems/wiiu/en_na/system_transfer_faq.jsp

To play Wii Only games it would kind of work if you have a sensor bar, but several games require the gamepad either somewhat (it's required for some levels in Super Mario 3D World but might not be required to reach the "final" boss) or entirely (zombiU and Nintendoland are unplayable without one), and the eShop is completely unusable without the gamepad. I really wouldn't recommend it without the gamepad unless you're using it as a Wii replacement.

Also I'm not sure if first-time setup requires the gamepad (not willing to factory reset to test), but the Settings menu requires it, so for sure you won't be able to set up Wi Fi, download system or game patches or access the digital game store ever. It's really not designed to be used without it and while it technically does not need the gamepad for all uses, it's really not a properly functional device without one.