Moving WP into pre-existing database

I installed WP onto the same server as my existing website (which is a free advertising site that also allows people to earn commissions for selling my products) intending to integrate the two, so that affiliates can promote the blog to advertise their own websites and also make sales of my products through it.

After using the installer to create a separate database for WP and playing around a bit, I think it will be much tidier if I move all the WP tables into the existing database.

Is this as simple as exporting the WP database using phpmyadmin, switching over to the existing database, and importing the WP database? Will this just add the WP tables to the existing database, and not make any changes to content that’s already in that database? (All the table names are obviously different.)

I’ll obviously back everything up before I do it, but the existing database is too big for phpmyadmin to handle, so if it goes wrong I’ll have to reinstate it using SSH, and I’m not very confident with that.