I don't think Hindi's phonology is more complex than English, but it is all explicit in the character set rather than implicit in the etymology. (The voicing difference between "this" and "thistle" is my favorite example of this, even beyond the fact that we're representing one of the most common consonant sounds in the language with two characters.)

In the World Atlas of Language Structures http://wals.info/chapter/1 , Hindi is considered to have a large consononant inventory. Hindi consonants plus vowels is not hugely different than English. But even though it's relatively large, I certainly wouldn't describe it as complex. It's mostly just the same properties repeated in different locations.

Language areas aren't made more complex by additional phonological complexity. The question you've asked seems to be "Does phonological complexity cause more language diversity". When put this way, there doesn't seem to be any causal mechanism that could do it. For instance, one might say: Well, English has a lot of vowels. People in California might simplify them one way, whereas people in Texas might simplify them in another way so that they can't understand each other well: therefore, you get additional linguistic diversity. But this requires the Texans and the Californians to be isolated from each other which isn't what people mean when they say "India is a very linguistically diverse country".

If we try it the other way "Does language diversity cause more phonological complexity", languages tend towards each other in case of diversity (because a person who speaks both Chinese and English will sometimes adopt features of one language into the other). This can sometimes lead to the propagation of more sounds (for instance, languages pretty much only use clicks if they're in contact with other languages that use clicks). And sometimes it can lead the elimination of them. I'm not sure of any particular research about this question, but my guess is on average it would tend towards the average, but if you took English and put it in India it wouldn't be too long before English in India sounds a lot more Indian.