Do apps in the Dock take up disk space?

No; the Dock icons are only shortcuts, and the applications need to be on an actual drive to work.

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While an icon in the Dock doesn't take up any storage, I'm sure the app exists on disk. Many apps install themselves into hidden directories on your disk. You won't be able to find them without help.

Why do you ask?

Press the Apple () menu > About This Mac. On the Storage panel, click the Manage… button. Then click the button Review Files in the Reduce Clutter section. You will see different tabs that will list files in descending order by size, and this may help you make gains in disk usage reduction.

Apps and other Dock items are actually icon aliases to the original application, or item, so no, Apps in the Dock take no storage.

DCarlson93 wrote:

I was looking for a way to minimize disk usage.

Other than Apple's own Xcode, there are very few apps that take up noticeable storage space. Apps may generate and collect data far in excess of their actual size. These are the files that are more likely to impact your disk usage. Unfortunately, these files are even harder to find and manage.

Can you clarify further? Are you having problem with disk usage? How much free storage do you have. Please note that the ONLY place to find out how much free storage you have is in the Disk Utility app. The Finder and most other methods flat-out lie about this.