For most sites, GZIP will not slow down a site. We use Cloudflare so we don't need to think about it, but only really heavy-traffic sites will see a performance hit from this.
Encoding in Base64 increases the file size, so this would slow things down. But it does make sense for really small images and icons because it decreases the HTTP connections required. I see this sometimes in CSS stylesheets where small arrows and icons are converted to base64. I'd be curious to see a comparison of Base64-encoded small images in CSS (sent using Gzip compression) compared to their non-base64 variants.