In HTML4, you were encouraged to wrap form elements in some kind of block level element, like a P or a DIV, but thankfully in HTML5 that seems to have been dropped, so if you are using the latest doctype, then there won't be a validation problem on that score.
Even if using HTML4, there won't be a problem with leaving out the Ps. Just a validation message.
<input type="text" placeholder="Name" name="u-name">
<input type="email" placeholder="E-mail address" name="u-email">
<input type="submit" value="Subscribe">