@maurymarkowitz
Using Multi-site, each site would be running its own individual instance of WooCommerce - WPMU 'Network Activation' of woocommerce simply activates the WooCommerce plugin on each site in the multi-site network, they are in no way linked apart from being able to share users.
(As an aside, network activation is buggy at the moment, it only prompts one of your many sites to install woo-commerce pages, after it's done on one site none of the others get prompted to install the pages even though they do not have them)
There is no "global" woocommerce install - the best you could do without a LOT of work would be a global custom post feed, aggregating all "product" custom post types across the network into a single archive / page for display - this would be "pulling" the products from the sub sites, there is no way to "push" products to multiple installs like you are suggesting (separate sub-sites pre region seems to be implied)
For your problem however, you could use the user's IP region (which woocommerce does a decent job of detecting anyway) to show or hide different products, product categories, or tags etc (essentially any meta could be used to sort these), a plugin would need to be written to handle this. It would make more sense seeing as you want to show/hide products from a unified list, not do multiple vendor aggregating like the other users are requesting.
I hope this helps
Aj