Not really, you can run sudo steamos-readonly disable to make it writeable, but that's not really advised.

The way you're supposed to install software is through the Discover store, which puts it in the writeable portion of the filesystem (only system files are read-only). That's a bit of a different way of the system than most desktop Linux distributions.

Also, you get whatever updates Valve supplies, whereas desktop Linux distributions will generally provide more packages and often more frequent updates. So your selection of system packages (the stuff that would go in that read-only filesystem) would be more limited than with a regular desktop distribution. Valve is probably only going to supply drivers for their products and whatnot, so you're going to be stuck with whatever Valve chooses to support.

But there's really nothing special about SteamOS. All of the important stuff is either packaged with Steam on desktop or submitted upstream (e.g. kernel and driver improvements), so you'll be getting that with any reasonably up-to-date distro. Save yourself the headache and just pick a mainstream distro and auto start Big Picture Mode on boot. Then you can use it for whatever you want and not be limited by whatever Valve wants to support.