This is a complex question as it covers operational, physical, and political areas.
There is little stopping you from using a single core to manage these providing you are willing to accept that the speed will be inmpacted due to the number of systems. When I mean impacted, I mean that being able to service this many clients, operators etc has load areas for query evaluations, directory queries, processing of inventory scans, and handling of thousands of policy requests each day. The single system will handle it without issue, it is just that someone used to a system with one thousand systems might feel the speed of response is a little low. Set your expectations correctly and performance will be fine.
In general, if you have centralised IT with limited remote IT presence, then a single core is good politically since central control is already established. If you have distributed IT presence with regional admninistrative controls, then multi-core might be best until such point you can approach a standardisation strategy. It will be more inefficient though.
Rollup cores are limited in operational use and are mainly good for inventory rollup. Some people I think make good use of the scheduling capabilities but I find them restrictive. Watch out for schema differences. You have to keep the cores at the same version levels or they become incompatible. This requirement can be difficult to maintain with a lot of cores where IT teams are fiercely independent.
I would suggest consulting with an ESP that has plenty of experience in this area. Items above are just a few of the things that need to be considered so it would be good to run possible designs past people with exposure to multiple environments. It certainly came in useful for me; I have a lot of experience myself but most from a single environment whereas consulting with an ESP with large environment experience (and in your case multi-national) experience could be pretty good for you.
Mark Star - MarXtar LANDesk Enhancements
Home of Power State Notifier & Wake-On-WAN for LANDesk