Do external stylesheets get loaded before the HTML?

If I have external stylesheets being included in the <head></head> section of my HTML page, will they be loaded before the HTML and immediately applied upon rendering? Let me present my specific use case.

External styles.css file:

form label {
    display: none;
}

Page containing form:

<head>
    <link rel="stylesheet" href="styles.css" type="text/css" />
</head>
<form action="process.php" method="post">
    <label for="name">Name</label>
    <input type="text" id="name" name="name" />
</form>

Can I be confident that the labels will be invisible upon page load (no flickering due to CSS downloading)?

Otherwise, I can add the style attribute inline, but that can be a maintenance nightmare.