Been using Meteor for 4 months, and I'm an junior ops guy turned developer. So if I say something that sounds like I don't know what I'm talking about, it's probably because I don't, so take it easy. Having said that, here's my two cents:
First and foremost, Meteor is a complete platform for building modern web applications. You get so much out-of-the box functionality that you'll be productive in no time. Also, you will find that your codebase is several times smaller than with other frameworks, because the isomorphic javascript saves you from needing to do a lot of boilerplate and configuration. You also have very convenient ways to organize code, whether through packages or in a /client or /server or /cordova folder, so you'll have an easier time managing your code. So a "big" application is smaller than it would be, and makes for more understandable code.
There are many, many examples of functionality that you get for "free" without further set-up, and in my experience it empowers you, the developer, to build richer, better applications.
I think that the fact that the platform is stable and past 1.0, and the package ecosystem at atmospherejs.com is vibrant and high-quality, the answer is yes you can absolutely build an application with a large code-base. (And, I might add, you may wonder why you ever did it another way.)
As for scaling, you're on a non-blocking node architecture, and so you're already doing pretty well. If you can't figure out how to scale it through the community, my understanding is that the folks at Meteor are working on a paid product that will make it dead-simple to scale to your heart's content. I am guessing that by the time you launch your Meteor-built product, there will be ample resources to hold your hand through it.