This article confirms that Intercom supports WordPress multisite for WooCommerce stores as of April 12th, 2023.
WordPress Multisite Support
The updated WooCommerce integration plugin supports WordPress multisite, enabling you to use Intercom with WooCommerce stores built using:
Multi-sites using sub-domains
Multi-sites using sub-directories
WooCommerce Integration Plugin Update
To use this feature, update your WooCommerce integration plugin to the latest version. If you do not use WordPress multisite, this update will not affect your integration.