No, given:

this is a line
this is line2

this is a new paragraph
this is line2 on a new paragraph
[download]

it will produce

this is a line
this is line2
<p>
this is a new paragraph
this is line2 on a new paragraph
[download]

I do agree that you probably should put a <p> tag at the beginning, but in HTML a <p> tag doesn't need to be closed. XHTML is another matter, ofcourse.

joost.