Potentially yes it is possible, in fact it would be possible with JobRoller, or even the
ClassiPress theme (both themes would allow people to create listings, with site visitors being able to contact them via the contact form on the ad/listing page). These themes are not encrypted, so you are free to modify as you wish. In this instance you may just want to read the overview and check the demos for both themes and see which contains more of the features you are looking for, as this would mean less modification overall on your part. One thing ClassiPress has that JobRoller does not, is that you can create a custom ad form, meaning your ad posters can complete whatever fields you require them to fill out.
Vantage also has this option, but right now it does not include a contact form on the listing.