In general, all Global mods do is help the moderators handling reports. Some global mods will also help with administrative duties such as temp bans, account recoveries and the like.
If there are sufficient section moderators, having additional global mods will not be necessary.
How many boards only have a global mod assigned to them?
I've noticed since the new reports page is available that when I report a newbie that all moderators can deal with the report is usually handled very quickly but when I report a Jr. Member or above it often takes many hours or sometimes even a couple of days to get handled. That's what I'm basing my opinion that the global mods are overworked on.
This may be the result of needing more board specific mods in certain boards. It may also be the result of certain mods declining to handle certain reports for one reason or another -- perhaps because they do not have time to investigate a report, because they do not agree with/understand an underlying rule, there is some conflict of interest, or some other reason.