Should I use WordPress to skin a database website?

WordPress is an ecosystem of its own, and it’s pretty fat in terms of memory use and existing APIs and structures.

Integrating this huge behemoth with a lean back-end that you have already built on your own won’t make much sense unless you specifically want to use WP’s back-end functionality instead of yours.

WordPress themes are just HTML, CSS, and JavaScript, so anything a WP theme does, you can achieve in your app as well – it’s “just” a question of effort. Starting to use WordPress just because of a nice-looking WP theme won’t make sense as the effort of integration will very likely be much more than what you save by using the theme.

If however you’re considering using WP as the back-end (say, using custom post types for aircraft entries, etc.) that is a totally valid path to go. Again though, it has pitfalls as well as advantages, and the ability to use some nice-looking WP themes shouldn’t be the only factor in your decision.