My instinct is to say no. But I can’t prove it.
It is generally accepted among scientists that animals have limited language capabilities. The majority of their communication is believed be visual (through body language). Vocalization is not thought to play a very major role in animal communication.
Also, since cats and dogs don’t attend school, their communication patterns are believed to be hereditary and instinctive. This means that in theory dogs and cats should be able to communicate with each other only minimally, since they only inherit the ability to communicate with their own species.
That said, nobody really understands the true degrees of communication that occur among (or between) cats and dogs. In the past, scientists doubted that animals had emotions or personalities, just as they now doubt that animals can communicate extensively with one another. Most people now recognize the uniqueness of individual pets, and it is becoming clear that animals lead quite rich emotional lives.
One thing is sure: some degree of communication absolutely is possible between species. For instance, no schooling is necessary for a human to recognize that a snarling dog should not be touched. And pets are quite able to recognize anger, sadness, and happiness in their people.