Is it possible to render CSS/JS files within Custom Servlet Plugin ? If yes

Can you please describe in detail what exactly you are trying to achieve ?

There are two ways you can render CSS/JS in Custom plugin, though Appian dose not recommend first way
1) By Keeping your CSS and JS file into Appian product base folder structure(ear\\suite.ear\\web.war\\..) and than refer these files into your HTML
<script type="text/javascript" src="js/your.js"></script>
<link rel="stylesheet" type="text/css" href="css/your.css">

2) By Keeping CSS and JS folder into same Plugin folder and refer these files into HTML
// To include CSS
<style>
#include("css/your.css")
</style>

// To include JS
<script language="javascript" type="text/javascript">
#include("js/your.js")
</script>

Have a look at com.appiancorp.suite.cfg.CustomBrandingService to refer style into your java servlet