Is it possible to pair a keyboard without entering a passcode?

As far as anyone can tell.... no you can't. There's no option for keyless pairing in Windows 10 and this feels like an OS level decision.

It might be a bug, it might be intentional, but unless someone can prove otherwise, you cannot do it in Windows 10.

Pairing without pin is possible in windows, but not supported by the default GUI. Take a look at ConfirmOnly option on this MSDN page:

ConfirmOnly

The application must confirm they wish to perform the pairing action. You can present an optional confirmation dialog to the user. With a value of ConfirmOnly, Accept the pairing if you want it to complete.

Microsoft provides code examples of applications with different pairing GUIs, which could be a starting point for someone with Visual Studio and some free time.