Sort of.
The characters you're describing are commonly known as radical-phonetic characters, where part of the character indicates the sound, and the other part implies the meaning or category. It is my understanding that Communist China's push towards character simplification has broken a great deal of phonetic relationships inherent in this class of characters, making the language much more difficult to learn than it used to be, even if it is marginally faster to write.
Additionally, there remain the 10% of characters which don't fit into this mold, a great many of which are very common.