I feel gypped.
Josephine made a very good point: that the identity of the secret admirer may have a significant impact on the admiree's opinion. Consider that the longer the secret goes on, the longer the person has to develop a mental image of the admirer. If the revelation differs significantly from the expectation there may be a very obvious negative reaction, even when they might have been willing to consider the same person if approached openly.
Assuming you are asking because you are considering doing this yourself, my question would be: how well would you handle rejection, particularly if it is reflexive?
Because of my personal experiences, I think the secret admirer thing is creepy. Anthony, just try to attract the girl by being yourself and asking her out if it feels right. I think handing her flowers in person out of the blue will make a bigger more positive impact than sending them secretly. If you do the secret admirer thing and she doesn't like you, you will feel like a bigger fool.
"You just walked in front of me with that pretty smile -- If you're unattached, give me a call. ###-####."
I thought it it was kind of cool and was impressed that everything was spelled and punctuated correctly.
I was a little uncomfortable actually responding because it happened less than a year after my husband passed away. I think I called the number but then chickened out when I got an answering machine. I have to give the guy props for a nicely written mash note, though.