No, Chinese keyboards usually have the same amount or fewer keys depending on the keyboard type they use.
iOS 7 lists 6 Chinese keyboard types, 3 of which can also be used in Simplified mode:
- Handwriting: user draws a stroke or character from which the computer recommends autocomplete options
- Stroke: user selects from a small set of character categories (around 10, including vertical, horizontal, &c), after which characters can be further specified
The other keyboard options are likely phonetic. The Japanese keyboard similarly uses simplified sound characters to further select the kanji. This is a bit different because these phonetic characters are part of two additional alphabets used in Japan: Hiragana and Katakana. They also use the Roman alphabet.