This would totally work!
First off, unless you are a regular Robert De Niro, she's gonna know you're full of s###, but she will be amused by this. Good first impression? You bet! It says you have a sense of humor, you're fun and spontaneous, playful, and creative. She's used to being hit on, probably in a variety of dull and predictable ways, but the curiosity alone should be enough to "see where it goes".
Besides, a good friend of mine once said "Whether they show good interest or bad interest, it's still interest, and interest is always good!" And from what i've learned, a good first impression (or bad) will automatically influence how they see you in times to come. Sure, you could redeem yourself from a bad impression, or even turn a good one sour, but it's much more difficult to do so. Imagine your favorite NFL team has 30 points on the scoreboard before they even start playing, and you'll have an accurate depiction of this. Sure, it's not unheard of for an underdog team to recover from a slaughter, but wouldn't it be nice to be 30 pts. ahead? Just act confident.
Keep the conversation light, and keep in mind she may challenge you about your dilemma (subtly letting you know she's "onto you" ). Keep your answers as surreal and creative as possible.
Even if she says no to a follow up, she'll still likely be thinking about you for some time. After all, you did pretend to lose a falcon just to break the ice, how flattering is that!