That said, you could probably use a synchronized random number generator as the shared pad data.

No; a true OTP is NOT the same as pseudo-random OTP. For an illustration of this concept, let's assume that your adversary knows your algorithm for generating the pads but has no information about the shared secret between you and your partner. To make things easier on your opponent, let's assume that he knows that you plan to encrypt a 1GB plain-text ASCII file.

In the case of a true OTP, you and your partner must share 1GB of data securely. Because the pad is truly random, any 1GB ciphertext is equally likely, so your opponent must consider every combination of 1GB, meaning 2^(8e10) equally likely ciphertexts. This is basically secure for all eternity. Also complicating the matter is that for a given ciphertext, all plaintexts are equally likely. So, the opponent doesn't know if you said "Attack the beach at noon" or "Attack the beach at dawn" or "jcfpeb k,spq djte96bslg1Hw"

Now, in the case of a pseudo-random OTP, let's assume that the seed of your PRNG is 32 bits, so you only have to share a very small secret securely. However, there are now only 2^(32) possible ciphertexts that the opponent needs to check. This is a much more practical problem, and he can use some simple checks to see if the decrypted message "makes sense", and choose the most likely plaintext.

In reality, nobody uses a OTP because if you can securely communicate the length of the pad, you can just as easily communicate the entire message. What is used instead is public-key encryption where your partner can encrypt a message, but only you can decrypt it. Of course, this is a few orders of magnitude harder than symmetric encryption, which is why you'll typically use the public-key encryption to share a disposable secret key, which is then used to seed a symmetric encryption method (your pseudo-random OTP would be one of those). In reality, this is still pretty secure, as the key is typically in the range of 128+ bits, meaning a key space of 2^128 for a brute-force attack, which is still pretty infeasible. However, it is not completely 100% secure against any decryption as a One-Time pad is.