If you use Brad's CPA redirector then the chances of the referrer leaking in most browsers is minimal. There are some browsers (mostly obscure mobile browsers) that you just can't blank or fake however. If you use lesser methods (eg. double meta refresh) then the chance is much higher because the way that browsers handle referrers is not standard.
The potential downside depends on your particular usage scenario. Most people fake referrers to hide their traffic source from affiliate programs, eg. if a program has banned Twitter traffic, and you want to send them some Twitter traffic you would then fake the referrer to something else. If you get caught you'll get banned but obviously it depends on your own particular situation and reasons for faking the referrer.
It's always better to fake the referrer to a nice clean full page ad rather than blanking the referrer; not sending any referrers is a huge red flag that you've got something to hide. Especially if you're a new account at a program, you can count on someone looking at your referrering urls before you get paid for the first time.