So I actually figured out a workaround for this. I'm posting it here in case it's useful to anyone else. I'm still not sure why "current.task.getLink()" won't work to grab a link to the sla's task record, but "current.task.sys_id" WILL work to grab the sys id of the sla's task record. With that knowledge I changed the script to use the task sys id to make a link in the script. The particular version of the script here will only work for records extended off the task table, but that should include most records that would have SLA's running on them.
(function runMailScript(current, template, email, email_action, event) {
var link = current.task.sys_id;
var backgroundColor = 'background-color: #278efc;';
var border = 'border: 1px solid #0368d4;';
var color = 'color: #ffffff;';
var fontSize = 'font-size: 16px;';
var fontFamily = 'font-family: Helvetica, Arial, sans-serif;';
var textDecoration = 'text-decoration: none; border-radius: 3px;';
var webKitBorder = '-webkit-border-radius: 3px;';
var mozBorder = '-moz-border-radius: 3px;';
var display = 'display: inline-block;';
var padding = 'padding: 5px;';
template.print('<br><font face="helvetica">');
template.print('<a href="' + gs.getProperty('glide.servlet.uri') + 'task.do?sys_id=' + link + '"');
template.print('style="' + backgroundColor + border + color + fontSize + fontFamily + textDecoration + webKitBorder + mozBorder + display + padding);
template.print('">');
template.print(gs.getMessage('Take me to the Ticket'));
template.print('</a>');
template.print('</font>');
})(current, template, email, email_action, event);
