Is it okay to compress application files? (Especially licensed applications)

Most macOS applications are not actually like 'any other file' - they just look like one - and are actually a folder of files called a package. Right-click on most apps, and you will see a Show Package Contents command. Click that to see the folder structure of the app.

That being said, applications will compress and expand just fine. I've compressed and expanded Adobe apps with no effect on licensing so long as they are expanded onto the same system.

Compressing an application and expanding it on a different system may break licensing if the licensing mechanism itself resides outside the app's package, or if some other licensing scheme is in effect. There is no generic licensing scheme for all circumstances.

Zipping is a lossless compression algorithm. You will not loose anything when going from Folder→ZIP File→Folder. You can even confirm this by verifying the checksum of a file before being zipped and after being unzipped.

Side Note:: If its difficult to understand how anything could be compressed without losing data here's a good way to understand it: "AAAABBCCC" can be compressed into "A4B2C3". The compressed string is 3 characters shorter then the original yet both still say "four A's, two B's and three C's". While this is not how the zip algorithm works, it is a good way to understand the concept of lossless compression.

To answer your question, while it is ok to compress a Application (which is just any old directory) the license file will most likely not transferred because most of the time it is not stored inside the application's folder. However, if the license file does reside in the application's folder than yes it will transfer. ZIPing the license file will not corrupt it.

Just an FYI: Most applications cannot be transferring by just copying the application. Most store files in ~/Library, /Library, or other directories. The application won't run properly without these directories and associated files.