does a saree cover the body well

defenitely, for an idian woman a sree is coolest thing to wear

Saree could cover the whole body if one wear it properly. Women wear saree differently and it depends on the person who wear it how she wear it. In my opinion it could cover the body very nicely and also give you a feminine look. But it is much easier to wear other dresses like suit or trouser or salwar kameez and it is not always convenient to wear saree like other dresses while you are travelling or on rainy days etc.

From an Indian Man's perspective I think the Saree covers the womens cody very well if worn properly. I have seen a few people very the Saree very shabbily and believe me it can be very embarrasing.