Yes.
You could be in the middle of doing important work and have the whole computer crash. Other than that, no problemo.
And some software might have security issues; updates to that software fixes those problems. So if you're not worried that Rupert Murdoch is trying to get your personal info, again, no problemo.
Seriously though, it only takes a short time to upgrade stuff these days. If you aren't inclined to do so, then freeze your system; in other words, don't upgrade anything since it all works now. You still may have security issues, but since everything already works with everything you're pretty safe. But stuff you access online, like video, will eventually not work well.
Rob