Let's look at the track record.
Backwards compatible handhelds:
- GameBoy Colour (to GB)
- Gameboy Advance (to GBC)
- Nintendo DS (to GBA)
- Nintendo 3DS (to DS)
Home consoles:
- Wii (to GC)
- Wii U (to Wii)
Not backwards compatible:
- SNES
- VirtualBoy
- Nintendo 64
- GameCube
- Switch
Lack of backwards compatibility to the previous generation has usually followed from a change in media format, and even then there has been a willingness to make an effort (the DS with its two slots being the prime example). Backwards compatibility seems to be a good way to ensure a wide selection of games at launch, and the negative aspect (not being able to sell the re-releases of the same games yet again to those desperate enough) seems to be outweighed by the positive (availability of games at launch; maintained interest in games from previous generation).
There's no real reason for Switch cartridges to grow any smaller, and I doubt they'll go back to discs. So I would say there's a pretty good chance of backward compatibility.