Is wp-content/install.php a Drop-in?

To answer your question, Yes

In fact, there are many other functions you can override in that file, it’s included as the first line of “wp-admin/includes/upgrade.php” & there are many functions inside to be overridden

Unfortunately, there is not too much information available regarding drop-in plugins but i’ll try to put a few points

1. They are distinct to normal plugins in the sense that they can’t be packaged & installed through wordpress admin.
2. Using them means the owner manually uploaded the plugin at the correct location. So it’s assumed that it’s written & added by the owner themselves.
3. These plugins are only meant to have code specific to the particular wordpress site.
4. Since they are added by the owner, they can’t be controlled (activated/deactivated) from admin panel. The include statement is hardcoded in the core.
5. They don’t need to have any file headers.

To summarize, they are php files hardcoded to be included(if exist), whenever the corresponding functionality is being loaded by wordpress.

To use them, just create a php file with that name inside the “wp-content” directory & it will be automatically included. That file can of course include any number of other files as needed.

EDIT

As toscho pointed out,
1) Drop-ins(if available) are also listed in the wordpress admin panel with all the other plugins. Though unlike other plugins, you don’t have the control to de-activate them from there.
2) WordPress, when upgrading itself(core upgrade), does not alter the “wp-content” directory. For this reason, these plugins never change between upgrades.
3) You can define a constant in the wp-config.php to change the “wp-content” directory to some other. The constant you need to define is WP_CONTENT_DIR. This also changes the defaults for other constants such as plugins directory, so you’ll need to take care of that as well, if needed