As you mention, yes you would need to do some customization of the theme in order to perhaps remove default fields that may not apply (i.e. salary, maybe others), but technically yes you could use it for this purpose. If you have the coding knowledge to do so, you are free to customize as you wish.
Alternatively you could also use the ClassiPress theme for a similar purpose, and you may find the custom forms and fields function useful to specify exactly what you want on the ad posting form. You can read more about the
ClassiPress theme here (as well as view the demo sites).
For both themes you should note that you can charge for the jobs/ads to be listed, but customers cannot pay each other through the themes by default unless you again customized them.
