EnigmaMaster

This was my setup to use the noaa weather widget outside of wordpress

<?php
require('Blog/wordpress/wp-blog-header.php');
require('Blog/wordpress/wp-content/plugins/noaa-weather/noaa-weather.php');
?>
then in the body i added

<?php
$test = new NOAA_Weather_Widget();
Get_NOAA_Weather_File_With_HTTP('KFMY');
$test->NOAA_Weather_Widget();
$args = array(
"name"=> "Main Sidebar",
"id"=> "sidebar-1",
"description"=> "Appears on posts and pages except the optional Front Page template, which has its own widgets",
"class"=> "",
"before_widget"=> '<aside id="noaa_weather-2" class="widget noaa_weather">',
"after_widget"=> "</aside>",
"before_title"=> '<h3 class="widget-title">',
"after_title"=> "</h3>",
"widget_id"=> "noaa_weather-2",
"widget_name"=> "NOAA Weather",
);
$instance = array(
"noaa_title"=> "NOAA Weather",
"noaa_code"=>"KFMY"
);
$test->widget($args,$instance);

?>

Actually yes you can. Tho you ll need a good understanding of php.
add require (‘path/to/file/in/wordpress/install/wp-blog-header.php’); at the top of the page thats outside of wordpress.

download the plugin and unzip, and put the plugins php file and css file if one in your root directory or where ever else you want it.
include the php file and link the css

you ll then need to go through the plugins php file and look thro the code and see how to call the plugin and what args might be required