You’d have to download the JavaScripts from Google either manually or using a cron job and a script to download them at regular intervals, and host them on your own site. It’s not recommended though. If you Google the topic, you’ll see a lot of conversations about why you don’t want to do that. In short, you lose performance because Google serves them faster.
Technically yes, every single script you add will mathematically add time to your site load. That’s the nature of having a website. The only way to have a truly instantaneous page load speed is to have a basic page with almost nothing on it. (Think: Google homepage) If your site loads in a second or under, you’re in good shape, as that is excellent.
I’m just saying that using a plugin like this, you have to go in with some common sense knowing that anything powerful enough to be able to translate your site into just about any language…on demand(!), is not going to be without even a small performance penalty. It’s a very powerful feature to add to a site if you think about it. You just have to decide the cost vs. benefit for your site and if it’s worth it to you. And really the performance hit is very very small for what it’s doing.
In our experience though, it’s not causing much performance penalty at all, so providing the ability for people all over the world to be able to read a website’s content in their language is very well worth it. For the sites we manage there was little to no hit on the GTmetrix scores with this installed vs without. (Keep in mind, all of these sites are very, very well optimized.)