Can I use WordPress to create webpages that connect to my existing database?

Hello,
I have a website which I’ve hand written using php, css, html, and javascript. I’ve also designed the relational database in MySQL.

Now I’ve gotten to the stage where I would like to change the look and feel of the website and I’m really impressed with the WordPress themes.

My question is can I use WordPress to create the look of my website, but keep the php processing files and relational database that I’ve already created?

Put another way:
I have php files that generate html files that users see when they visit my website. These files have forms, which post data to my server. The files that process this data manipulate it and insert it into a MySQL database.

I want to keep my files that process this data and insert it into the database. I also want to keep my database. I just want WordPress to create the page that my users see.

Is this easily supported or is WordPress not for me?

Thanks!