Does a blank plugin come with any overhead?

No, outside of purely technical aspects of PHP includes (as you correctly pointed out), there is no additional overhead to plugin quantity on general WordPress core load..

The list of active plugins is calculated in advance and stored persistently. The load process just runs over it and performs PHP includes on each.

The edge cases where it does take longer are mostly related to plugin management:

  1. Some screens like plugin list (obviously) need to re–scan all plugins and extract data.
  2. Update checks need to scan for data to submit as well, though with them the network request being made is likely bigger bottleneck.

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