Is this practical?
If you'd like to take advantage of all WordPress has to offer with regards to content organization, searching, a user-friendly back-end, easy extendability through plugins and themes - then yes, very practical.
If you just want to use WordPress themes/templates, then no - it would be somewhat insane to maintain a separate database, separate search functionality, and try to tack your current code onto WordPress just to display your site with a WordPress theme. It would be far, far more efficient and sensible to find a plain HTML/CSS theme and simply apply it to your site.
Would I somehow embed my PHP code inside WordPress pages?
A common approach would be to port your data into the WordPress database using WordPress's Custom Post Types and Custom Taxonomies, then create your own theme from scratch or modify an existing one using a child-theme in order to produce the markup you're after.
You could just hack your current code into theme templates - but that would largely defeat the purpose of using a WordPress theme in the first place, I'd imagine.
You could also just load the WordPress blog header (bootstrap) in you app to gain access to the WordPress environment - but again, kind of pointless if you're not intending to use any of WordPress's features.
Long story short, I'd recommend you spend some time reading up on WordPress before you commit to it. It doesn't have to be all-or-nothing - but in your situation I don't think the grey area makes a lot of sense.