Absolutely! A bird strike CAN take down a 747. They take down small fixed wind and rotor-wing aircraft all the time. ...
I can't help but feel that if that was the case, we'd hear a lot more about it.
Aircraft coming down is quite rare given total number of flights, and a google search for bird strike damage shows plenty of times a bird has hit and made a mess, but apart from perhaps "taking down" a plane in the form of forcing it to turn back to the airport and doing a controlled landing after receiving damage, I can't find too many instances of genuine bird strike causing the catastrophic form of taking down planes or choppers.
Having seen how fragile these Phantoms are to even just a fall from a few feet, I imagine propellers or rotor blades on full size aircraft are going to slice through one of these things like a hot knife through butter. It's not like props and rotors are made out of balsa wood, they're designed for millions of faultless rotations and surviving huge centrifugal forces, and almost certainly bird impacts are generally factored into designs as well, so I tend to side with the quote I've seen going around from someone in the military drone world, that said something along the lines of the result is minimal on the aircraft, and the drone destroyed. Mind you, I imagine even the tiniest dent on the blade of a Bell Jetranger, probably costs a crap load more than I'm ever going to be able to pay, so I'll drop my bird with a CSC even if that destroys it, before I'll risk being hit by a full size aircraft of any sort. Either way the phantom would be toast, but the bill will be a lot smaller if it hits the ground rather than an aircraft.
EDIT: Just found this:
"Nearly 500 planes have been damaged by collisions with birds since 2000, according to the Federal Aviation Administration. Some 166 of those planes had to make emergency landings."
15 years, and only 166 planes had to make emergency landings, and most of those seem to have had MULTIPLE strikes, in that they hit a flock, or in one unlucky case, two birds but managed to take out both engines at the same time.
11 a year might seem like a lot, but given how many flights there are per year, it's a percentage that is microscopic.