It happens to me, so it can happen to them. I visit a website, it loads partially, and stalls. Down in the status bar I see the message “waiting for www.google-analytics.com…” and it just sits there.
The next time a potential client comes to me for “optimization” of a site that loads Google Analytics before it displays the corporate message, I am going to assume two things: 1. They don’t try very hard before asking for help 2. Even if I do my best work for them, they will likely drop the ball when it is passed back to them.
It’s ok. Really. I’ll fix it. But that’s not SEO, and you really should consider looking for a new web design firm.