visualforce page ActionFunction reRender not Working

You can absolutely rerender the <use>and <svg> tag by:

The xmlns= on the div containing the SVG is a MUST as if you try to rerender without it the page will simply stall. Important trick to remember for anytime you are re rendering a container containing an SLDS SVG

How to convert a Visualforce apex:pageMessages to be lightning style

for example:

<div id="err_wrapper"
             class="slds-notify slds-notify--alert slds-theme--{!alertType} slds-theme--alert-texture"
             role="alert">
            <h2>
                <div xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
                    <svg aria-hidden="true"
                         class="slds-icon icon-text-email slds-icon--small slds-m-right--x-small">
                        <use xlink:href="{!URLFOR($Resource.SLDS, '/assets/icons/utility-sprite/svg/symbols.svg#' + if(alertType = 'success','check','ban'))}"></use>
                    </svg>
                    <span id="err_text"></span>
                </div>
            </h2>
        </div>

In this case I rerendered the err_wrapper