RE: Will multiple service tier servers improve windows client performance across the globe connecting to a single database?
In this scenario (single database, N companies in different locations), using N separated service tiers for the different companies is the best way to do (you can decouple users, tasks on a company don't disturb tasks on another company and so on). This is absolutely the recommended way to do.
Regarding service tier location, it depends :) My suggestion is to leave service tier as close as possible to your database. So, you could have a scenario where you have NAV database (SQL Server) on a server A and Service Tier 1,2,3...N on separated servers on the same network as the database server. Windows Client from different companies will connect to the respective service tier, maybe using a VPN. This is the scenario with best performances. Obviously, you need to check the network latency of the different companies.