Without the site search:
People type in your brand, see your site and click through. They find your product/service by browsing your site or using your site search. They get exposed to your brand and sales messages. Many will buy other items they see, or sign up to newsletters.
With the site search:
People type in your brand, and see the instruction to Search <YourSite>.com. Some will click on the link as normal, others will pause for a second, then give the site search a go instead.
70% of those doing a site search will get results. 2% of these will automatically click on the first thing that comes up (1% will correctly bypass the ppc ads, 1% will accidently click through to a competitors site).
Of the other 98%, most will start to question your brand at this stage. Is it more important to me to go with your listing - am I THAT loyal, or should I try some of those very appealing PPC adverts?
Id say 50% of them will click on a a competitors advert (the lure of 60% off being too great), while the other half will click on your link.
Now returning to the 30% of people who did a site search but didn't get any listings. When ppc adverts appear, roughly 26% will click on a ppc advert instead (its the next easiest thing to achieve what they're looking for, given that the site doesn't have what they wanted).
The others will type in a different search (or brand) into google and search again.
For pages that didn't have ppc ads, all will do a a different search into Google.
(note that the stats are pure estimates, and that I'm assuming that normal people assume that the site search searches all your pages and all your product/xml content, which obviously it doesn't)
Things become more complicated with Site Search! - but to me its clear that you'll end up losing traffic and customers.