Hanzi pronunciation by radicals
It is possible in Chinese as well, and similar rules apply.

The big reason behind this is the liushu 六書, or the six methods by which all Chinese characters are created: pictogram (象形), simple ideogram (指事), compound ideogram (會意), rebus (假借), phonetic-semantic (形聲), and transformed cognate (轉注). The method of reading by radical is only applicable to the phonetical-semantical category. However:


pictograms and simple ideograms make up a small (although very frequently used) portion of Chinese characters due to the poverty of these two methods in conveying relatively complex ideas. Pictograms and simple ideograms are one-piece in their own, and have no phonetic and/or semantic radicals;
rebus and transformed cognate characters are rare, and their origins relatively obscure;
a good percentage of Chinese characters are compound ideograms (in Japanese kanji, virtually all kokuji are compound ideograms). However, radicals for compound ideograms usually carry no phonetic value.


Fortunately, the rest, or phonetic-semantic characters (形聲字), make up the vast majority (>70-80%) of Chinese characters. So, yes, you may read them by radicals (but very carefully). However, in Chinese, the onset (聲母) and tone of many 形聲字 have changed, so their onset and tone is often different from the onset and tone of their phonetic radical (聲旁). Let's take characters in the phonetic series 方 as an example:


方 "square": Standard Mandarin fāng, Standard Cantonese fong1, Japanese go'on hō (ホー), Japanese kan'on hō (ホー). Reconstructed Middle Chinese (according to Pan Wuyun 潘悟云) /*pʷiɐŋ/, reconstructed Old Chinese (according to Zhengzhang Shangfang 鄭張尚芳) /*paŋ/.
訪 "visit": Standard Mandarin fǎng, Standard Cantonese fong2, Japanese kan'on hō (ホー). Middle Chinese (Pan) /*pʰʷiɐŋH/, Old Chinese (Zhengzhang) /*pʰaŋs/. 
旁 "side": Standard Mandarin páng, Standard Cantonese pong4, Japanese go'on bō (ボー), Japanese kan'on hō (ホー). Middle Chinese (Pan) /*bɑŋ/, Old Chinese (Zhengzhang) /*baːŋ/.


We see that reading by radical usually works in Japanese, but can be tricky to apply in Chinese. As a rule of thumb, use radicals to help remember the rime (韻母) part only. You still have to memorize the onset and tone. Moreover, since many of the onsets have already changed in the Old Chinese era, so really memorized the onsets when reading by radical.

Even with Japanese, reading by radical is not entirely bullet-proof. It can't help you distinguish go'on vs kan'on (which can be tricky), and it can't help you decide when to use on'yomi and when to use kun'yomi (also tricky).

PS: Standard Mandarin refers to Putonghua 普通話 and Kuo'yu 國語, which are both standard registers of Mandarin based on the dialect in and around Beijing. 普通話 is the standard in mainland China and 國語 is the standard in Taiwan: they are essentially the same language, with some disagreements on the pronunciation of a few words. Standard Cantonese is the de facto lingua franca in the Cantonese-speaking world, and is based on the Canton/Guangzhou dialect. Go'on 呉音 and kan'on 漢音 are both on'yomi/borrowed phonetic readings of Chinese characters, go'on being the earlier version.