Trackers are not spreadsheets, they are simple, custom, one table (thus typically denormalized) databases. Having said that you can get creative and link Trackers together but this then increases the administrative complexity.
Trackers are very powerful for what they do, although they are no full-on database. You would be able to filter trackers based on field criteria (for example a department field), and Trackers are searcheable too. I think as a large address book/staff directory Trackers would work just fine.
In addition, you can tie a particular Tracker to registration so that some/all tracker fields are requested at registration time, placing the burden of data entry on the user, rather than the administrator.
As for file galleries, they can be organized as mentioned hierarchically, and viewed with an explorer, tree-like interface or as a flat list. In addition, file galleries can be categorized with Tiki's notion of categories, which applies to many Tiki objects such as Wiki pages, articles, forums etc.
I think in general, an honest assessment of Tiki as an Intranet would be that it's a great fit because there are so many features built-in (no additional plugins/modules/widgets required), which is uncommon which you compare with applications like Drupal and Joomla. Having said that, it also means Tiki can be very complex. Naturally, you do get high levels of customization though, so it's a trade-off. I have found that setting Tiki up to the exact specifications you require can be very time consuming and sometimes infuriating, but in the end the effort is worth it because you end up with something that works for you.