My website will have users from all around the globe not 1 location. I know that I can put my file assets on a globally distributed CDN, and those files will be served from the location closest to the user which will lower the latency.
Is it possible to do the same thing for a (Mongo) database? Or does one still need to pick one location for the database and just put up with increased latency for users who are far away?
It is possible but you may want to put special attention on the headers that you DB/service will return especially the ones regarding caching like Cache-Control: max-age=<int> you would like to avoid the CDN behave just like a plain proxy with no caching capabilities.
In many cases, the CDN obey origin headers but if they are too small, they may be overwritten by some defaults that based on the plan/price could be adjusted.
Some CDN's allow prefetching based on custom times keeping always data updated. This could be useful in some cases and avoid flooding the DB with too many connections besides also restricting access to the service/DB only from the CDN and trusted sources.