That's a great question that I wish more people would ask! The answer to your question is both yes and no. When there are two agents with the same brokerage - one representing buyer and the other representing the seller - the basic rule of thumb is that neither agent can disclose information to either party that may damage the other party unless those disclosures are part of the agent's/broker's normal disclosure duties.
Here's an example: The seller contacts his agent and tells him "I'm listed at $200k but I'll take $150k". The agent cannot disclosure that information to the buyer or their agent, and if the buyer's agent becomes aware of that information, he or she cannot disclose that to their buyer. So in this limited scenario, the answer to your question would be yes. As a seller in this situation, your interests would be protected.
The opposite is also true: The buyer contacts his agent and tells him "I am offering $180k but am willing to go up to $220k". The buyer's agent cannot disclose to the seller that the buyer is willing to pay more, and if the listing agent becomes aware of this information, he or she cannot disclose that to their seller. Again, this is a rare circumstance, but in this case the answer to your question would be no, and as the buyer your interests would be protected.
We have represented both buyers and sellers at the same time and have never run into any issues. I would not be too worried unless there is a specific situation about which you are concerned. If you had the same situation with two agents from different brokerages, the likelihood that either agent would be in possession of inside information from the other side is extremely unlikely, but if they do come into possession of such information, then there would be no limitation on sharing that information with you.