Mine does!
I got the idea for this post from Gwen's blog After the dress...
I have a Viking 500 from about the mid-'90s, and it has a free-arm function. It also has a bed extension which I usually leave on. Here's what the machine looks like with the bed extension attached:
Here's what the machine looks like with the bed extension removed:
Here's what the machine looks like with the back of the machine bed removed to reveal the free arm: