No, probably not. I can't imagine that the switch will do it the same was as the PS4 does.

The PS4 fully installs all games to the HDD for performance reasons, seeing as optical drives are very slow. A game cartridge for the Switch will undoubtly be significantly faster than the PS4's optical drive, perhaps even faster than the PS4's HDD, so installs will likely not be required.

However, as a person who prefers digital for most things these days (and especially on a portable system. i don't want to bring with me several game carts that i could lose), I'm going to be screwed by the Switch.