No, only the Squier (and other MIDI-guitars) will work.
From Game Informer, Issue 209 (pg 32):
"Due to technology in the neck the Squier does not need to be re-tuned to alternate tunings," Baker assures us. "No capos are needed to play the game." ... Baker says you don't need to be in tune to play the game.
...
"The Rock Band 3 Squier Stratocaster uses technology built into the neck and fingerboard of the guitar to track finger positions in real time," explains Baker. As a player holds down a particular fret and string, the onscreen display will show that note and string, giving players feedback on correct finger placement even before the note is picked.
What all this means is the game tracks where your fingers are and when you pluck, not the sound the guitar makes.
It's theoretically possible that an accessory could be made to play the game using only the sounds made by a guitar, but doing this is notoriously difficult (and impossible in truly real-time - see this page and @Jeffrey's comment below), and would likely be very inaccurate and frustrating.
I've looked all over for the converter mentioned by @jblaske in the comments above, but can't find anything. He is probably thinking of the Rock Band 3 MIDI Pro Adapter, used to play Rock Band 3 with midi-keyboards and midi-guitars (not the same as electric guitars!).
It seems Minamimoto's is the best solution. Last year I bought Rock Band 2 Special Edition (bundle with one guitar, one mic and one set of drums) for $99 on GameStop, but they don't seem to be making that deal at the moment (at least not online). On Amazon, it's $113. The Beatles instruments are prettier, so I think this set is worth the extra buck.
As for the other instruments, consider getting Lips. At $30, they come with 2 wireless microphones.
Harmonix is only selling one Rock Band 3 bundle, with the keyboard controller, so I guess you don't have much of a choice there. And it's sold out at Amazon, which is even worse.
As for the cymbals, both RB2 cymbals and the new Pro Cymbals are being sold by the same price, $40. The only issue is that the new Cymbals will only be released on October 30th. According to a review, the new cymbals are much superior, so it might be worth the wait.
The only thing missing is the guitar. There are several options. You could pick a RB2 Wireless Guitar for $60, not much to go wrong there. With $20 more, you could get the Beatles Guitar, which could be nice if you get the rest of the set. If you prefer the Guitar Hero controller, it would be the cheapest option, at $50. And, for $70, you can get the Guitar Hero: Warriors of Rock guitar bundle.
You'll be spending at least $360 on all this stuff. But your parties are never gonna be the same. :-)
EDIT: Ah, and if you want to crank it up to eleven, get this setup.
Best Answer
In short, yes. A good friend of mine has tested this for me as he purchased the same kit. Just remember to plug the pedal in!