Sync user info from WordPress to external database

Theoretically possible, yes. The mapping code is all exposed in the plugin.

<tr valign="top">
    <th scope="row"><label><?php _e( 'User table' ); ?></label></th>
    <td><input type="text" name="pp_db_table" value="<?php echo get_option('pp_db_table'); ?>" /></td>
    <td><span class="description"><strong style="color:red;"><?php _e( 'required' ); ?></strong></span></td>
</tr>

So just map the additional entries… but that only handles the MySQL side. The user template modifications will be a little more hands-on.

No that is not possible because there would be some sort of collision along the way.