Can a large amount of CSS using  tags in a template file slow page load time?
Significantly? depends on how much is your definition huge. 

It's best practice to have your style's in CSS file because the browser can cache it. Therefore, on subsequent page loads it doesn't have to download your CSS file again. 

The browser doesn't cache your HTML, so it would have to download your huge HTML each and every time.

Caching off



Caching On