Would a symmetric cipher with a keylength a big as the data length be information theoretically secure? One-Time-Pad is information theoretically secure as long as the random number stream is evenly long or longer than the data stream it encrypts, for a "deciphered" message could have been any message with the same length as the given with the same probabillity. Does the same apply to symmetric ciphers, too? 

For instance if I have 1024 bits to encrypt, break it into chunks 128 bits and encrypt it with AES-128, each with a different (assume: true) random key,
will that be information theoretically secure just as OTP?
Or would a hypothetical algorithm (let's assume it would be as quick as the encryption function) impact the (theoretical) security?

In other words: Does using a symmetric encryption algorithm (such as AES) lower the probabillity of a ciphertext being originated from a specific plaintext even if the used key has "OTP-length" and is completely unknown?
No, using any keyed permutation with key length equal to the block size reduces the number of possible plain texts by ~1/3

Assume first that AES reasonably approximates a pseudorandom permutation, for each block of the message, the attacker (assuming unbounded computing power) can calculate the plain text for all keys. This is equivalent to throwing 2^128 balls into 2^128 baskets randomly. There will be collisions. The chance that any plain text is not a valid solution is approximately 1/e 

filled fraction = 1-((n-1)/n)^n , n=2^128

this converges to 1-1/e

this reduces the effective number of plaintexts by  about 1/3 (=0.63 ~= -0.66 bits). The reduction also tells the adversary about the probablity of any ciphertext being correct since about half the remaining plain texts got two hits instead of one with 2x the probability of being correct.

A problem with this scheme is that fooling the observer into accepting a plausible fake message requires solving for the key K which would connect the plaintexts and ciphertexts, fortunately, thanks to the recent SHA3 competition the cryptanalysis to do so has been mostly done.