No, use is a compile-time directive and so even compile-time errors will be caught. But errors from lines of code that get compiled before the use CGI::Carp line of code gets compiled cannot be caught.
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<code> <a> <b> <big>
<blockquote> <br /> <dd>
<dl> <dt> <em> <font>
<h1> <h2> <h3> <h4>
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<sub> <sup> <table>
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Snippets of code should be wrapped in
<code> tags not
<pre> tags. In fact, <pre>
tags should generally be avoided. If they must
be used, extreme care should be
taken to ensure that their contents do not
have long lines (<70 chars), in order to prevent
horizontal scrolling (and possible janitor
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or How to display code and escape characters
are good places to start.