Saves outgoing mails in a post type, drop it into wp-content/mu-plugins.

debug-mail.php

<?php
/**
 * Plugin Name: Debug Mails
 * Description: Saves outgoing mails in a post type.
 * Author: Dominik Schilling (ocean90)
 */

function ds_register_cpt_mail_debug() {
	register_post_type( 'mail-debug', array(
		'label'                => 'Mails',
		'show_ui'              => true,
		'public'               => false,
		'show_in_menu'         => 'tools.php',
		'show_in_nav_menus'    => false,
		'show_in_admin_bar'    => false,
		'publicly_queryable'   => false,
		'can_export'           => false,
		'register_meta_box_cb' => 'ds_register_meta_box',
		'supports'             => array( '' ),
	) );
}
add_action( 'init', 'ds_register_cpt_mail_debug' );

function ds_register_meta_box() {
	$post = get_post();

	add_meta_box(
		'mail-content',
		esc_html( $post->post_title ),
		'ds_mail_box',
		null,
		'normal'
	);

	remove_meta_box( 'submitdiv', null, 'side' );
	remove_meta_box( 'slugdiv', null, 'normal' );
}

function ds_mail_box() {
	$post = get_post();

	// Fix <http://...> links
	$mail = preg_replace( '#(?:(<)(https?:\/\/(?:.*))(>))#', '$2', $post->post_content );
	$mail = make_clickable( $mail );
	?>
	<pre>
<?php print_r( $mail ); ?>
	</pre>
	<?php
}

function wp_mail( $to, $subject, $message, $headers = '', $attachments = array() ) {
	return wp_insert_post( array(
		'post_status'  => 'publish',
		'post_type'    => 'mail-debug',
		'post_title'   => $subject . ' (' . $to . ')',
		'post_content' => $message,
	) );
}

function ds_remove_edit_actions( $actions ) {
	$post = get_post();

	if ( 'post_row_actions' == current_filter() && $post && 'mail-debug' === $post->post_type ) {
		unset( $actions['inline hide-if-no-js'] );
		$actions['edit'] = '<a href="' . get_edit_post_link( $post->ID, true ) . '">' . __( 'View' ) . '</a>';
	} else if ( $post && 'mail-debug' === $post->post_type ){
		unset( $actions['edit'] );
	}

	return $actions;

}
add_filter( 'post_row_actions', 'ds_remove_edit_actions' );
add_filter( 'bulk_actions-edit-mail-debug','ds_remove_edit_actions');