An operating system is like a table.
A browser or other application is like an item on top of the table.
Internet Explorer is an application, but it's PHYSICALLY part of the table because of how Microsoft bundled it with the OS.
Even if you don't use IE you really need to install updates. If a hacker gains entry to your system, they may attempt to abuse a known vulnerability that you could have patched but didn't and then your problem is compounded. Additionally, since IE is a shell used by some other browsers (and other applications), if you're using one of those tertiary browsers (such as Maxathon) you would be stuck with an older version of IE that renders the pages (even though the interface is something else).
When dealing with vulnerabilities, you need to do a cost/benefit analysis; does the cost of the downtime to install, and any compatibility problems it produces, outweigh the risk or loss incurred from an attack?
22Yes; You should update IE even if its been disabled. Yes; There are security concerns if you don't. – Ramhound – 2014-05-02T18:50:00.373
5The real question is why SHOULDN'T you install the update? Does it interfere with an application you need to use? Otherwise, if it makes your computer safer... – WernerCD – 2014-05-02T22:15:25.753
7Some games/applications may use the system browser engine (IE on Win) for background tasks, or as a "skinned" browser. Steam formerly, for example. For this reason, updates to the browser are always a good idea. Just to add, you can delete IE, but it's hacky :) – Jongosi – 2014-05-02T22:44:58.120
8Internet Explorer is not a standalone piece of software like FireFox or Chrome. It is a part of the Windows OS. Which is why it is a massive headache as well as a security nightmare. You are right to not use it, but you cannot predict when Windows will decide a part of it must run whether you know it or not. – JakeGould – 2014-05-03T05:41:49.433
1Be aware that disabling IE may affect other software. I've learned that the hard way after wasting a couple of hours trying to install Corel Draw. The installer uses IE to display the EULA. – Dennis – 2014-05-04T16:42:03.407