Should I install Internet Explorer updates although I disabled it?

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?

Other things use Internet Explorer that you may not be aware of, so if there are security updates for IE you should install them.

Other applications use scripts and pieces of the IE application.

I don't know exactly how it works, but yes you should install the IE updates.

You should always install updates for Internet Explorer, even if you're using a different browser.

Internet Explorer is very tightly woven into the fabric of Windows. For example, Internet Explorer's proxy settings, the hosts file and Windows Firewall are examples of parts of Windows that are intertwined with Internet Explorer. A vulnerability here puts your whole system at risk.

Additionally, as you can't uninstall Internet Explorer, it can run and make your system vulnerable. You don't know when it will run. For example, if you're viewing a Help file (.chm), Internet Explorer is rendering the page for you. Some browsers and other applications use Internet Explorer under the covers to render rich content. Again, a vulnerability here puts your whole system at risk.

I would absolutely suggest installing the update. IE is rather tightly coupled with the operating system and parts and pieces can be used by a surprising variety of applications. Even if you're not browsing with it on a daily basis, it's still on your system and is still a security hole.

More importantly, what's the risk/return on not doing it? The value of not doing it is not having to restart the machine. Meanwhile, if IE accidentally gets launched or is used without you being aware, it puts you at risk.

Just because you don't plan to use one of the pockets in your pants, if they have a hole, you should still patch them!