I think that depends on the "wrap" setting you use in your textarea tag.
Various browsers implemented wrap in different ways, and as far as I know default textarea behaviour in IE is to "soft wrap" the text, meaning the textarea box does not scroll horizontally and the text is broken into chunks that fit into the box without introducing line breaks into the text.
This would be equivalent to wrap="soft" or no wrap tag at all in IE.
Hard wrapping is when the browser introduces line breaks into the text at the point where it must be broken to fit into the box. I believe hard wrapping is NS's default in most versions.
wrap="off" would mean that the box will scroll horizontally as the user types and line breaks would only be inserted when the user hits the enter key.
The wrap="virtual" and wrap="physical" attributes were implemented by NS but never widely used, so I would say there is no absolute method of insuring your line breaks are implemented correctly on the client side.
Due to the differences in default browser behaviour, I prefer to keep "soft" wrapping on and then force my line breaks server side.
Hope this helps.