No, it covered the outside of the chain. It had 3 segments: the rear extending up to the chainring and derailleur, a disk on the outer chainring, and an arc covering the front of the outer chainring. The goal was to protect the pants from chain staining. More extensive protection, including the rear, could be developed, but the problem could arise from gaps through which debris could enter and accumulate over time. Single-speed Dutch bikes use plastic shells that encase the entire drivetrain. Even if you obtained such a shell, it would limit the drivetrain you could use.

On that topic, on my folding bike in winter, I encountered wet snow filling the gaps between the 11-speed cogs, making them unusable except for the largest one. The snow was coming down into those gaps from the fender above.