.maintenance and maintenance.php also in multisite install?

I would like to customize the standard maintenance page which gets shown during plugin updates.

For single sites the process is clear to me. Putting a maintenance.php into /wp-content.

But how does this work for subsites of a multisite install?

It works for the whole network, not for a specific sub site. Basically that mechanism is intended to be used when there is a software upgrade, time in which you don’t want to have visitors on the site that might result in some data corruption (especialy logged in users, but not only).