Some might but not 'all' - if you buy something from me it will show what you have bought - if you buy from someone else it may not -if I buy something that someone has made 'private' then it will show up on my feedback as a Private sale if I buy something the seller has not listed as Private then it will show up what I've bought in the feedback
The buyer has no control at all over the fact the item is private or not.
however -I have seen more and more things sold privately much more than used to be. Either the sellers are just forgetting to un click the 'private' when they list something, or people no longer wish to advertise what they are selling (stolen goods?)
BTW I sell hundreds of pounds worth of stuff on Ebay per month but use a different account if I'm buying