Does High Frequency Randomisation of valid and dummy messages in a high volume channel add security?
In addition to Paul's analysis, I'd point out that theres a few other issues.  The primary one is that, at best, you have increased the workload of your attacker by a factor of 1000, in exchange for increasing your own work load by a factor of 1000.  Let's say you're using a very poor encryption scheme that's known to be breakable in, say, 2^50 operations.  (after all, that's why you're relying on this obscuration right? because you didn't trust your crypto?)  Now the attacker needs to spend 1000*2^50 2^59.9 operations to crack it.  For the amount of extra resources you applied to send that much extra fluff data, you didn't get very much of a leg up on your attacker.

Worse, if your encryption is as bad as you think it might be, there's no guarantee that the attacker must fully process each message to discard it.  It may be very easy to identify which message is real because you may be able to identify the signature of the broken cryptography in the first place.

Finally, consider that you are absolutely dependent on the quality of your random number generator.  If you have a PRNG like that, and you have resolved all of the synchronization issues that Paul mentioned, you might as well have just used the PRNG to generate a one-time-use pad.  It would give you more security for less trouble.