OK - so I’ve got EE doing my bidding nicely, however one of my clients is a recruitment business which advertises vacancies. It would be easy enough to customise a blog to accept job details, however, my client uses a specialised recruitment system with a MySQL db.

Can I get EE to query this if I had the details?

Sure. You could make queries using PHP, right?
Just turn on PHP parsing for the template that you are using and then you are ready to go.

http://expressionengine.com/docs/templates/php_templates.html

sure, SELECT * FROM database.table works in EE,
so you can manipulate tables outside the EE database.