Short answer,as well as everything else, its not likely to be enforceable, simply because you didn't present it as part of the license.
Let's look at your idea, and start from basics, the license itself.
Your software will have some license attached. You've suggested Apache2. So somewhere there will be a file that makes clear, "this following text below, is the license", or else, "in this named file is the license".
The user has to know that that's the license. As an extreme example if your source code is 6000.files and contains a file called "/tmp/cache/trash/oldcode.php" that actually contains unannounced and without header, the license text, and nothing points to it as being such, probably no court will agree its binding on a user, because that's just not reasonable to assume. (They might instead stipulate that this means no license was granted, but the point is, the license must clearly be identifiable as such, by a reasonable user, to be enforceable)
So you need to provide a file or document that's clearly and obviously "the" license. That could be a top level file or directory called "LICENSE", or a config file item that you have to change to "yes" to confirm you read a specific named file, for it to run, or a first-run UI. I've seem all 3 of those, used. But the user has to agree to something specific, in a legally unambiguous definite way.
And that's your problem.
- If that file is the Apache2 license terms, it won't include your clause.
- If it includes your clause, then its a custom license not an Apache2 license.
- If you try to stuff your custom terms in a README file, firstly there's no legal obligation or reason a conscientious user would have had to read and agree that file. So its not legally binding. Secondly the license is this other file over here - it says so! - so clearly that README whatever it says, and whatever anything else.says, it isn't the license agreement or any part of it, because the license is this text here, which doesn't state that other text is to be included. (And if it did, then once again it wouldn't be the Apache2 license text..)
It fails whatever you do.
Your 2nd legal problem
The 2nd legal problem is that you are trying to DIY a legal text. That means that aside from any issue of user reluctance about a modified/custom license, and aside from stuffing text in some other file and trying to claim "its part of the license anyway", you have a second problem.
You need to be able to define, in terms adequate for a court to take note, exactly what may and may not be done with your code. Exactly how the restrictions will.work, to draw a precise line what makes it valid or invalid use, no ambiguity or inadvertent errors in a legal sense that could make it unenforceable. I honestly would say, don't even think of it. Even the simplest term is not obvious.
Example: Say you just wanted to say "not be used in any company with over 10 employees". Simple, right? How can that simple a clause have a loophole? But what about a 1000 staff company with a separate group company of 9 that would use it on behalf of them all? What if they have 8 staff but outsource all the rest to a contractor with 500 staff on their project? Just making the point, legal text stuff is NOT for amateurs. Even seeming simple terms are not.
And finally your 3rd legal problem
As stated, you can't copyright/license a pure idea anyway. Only a specific implementation of it (your own code). Meaning you can't copyright the idea of a database, an audio editor or a file archiver, the idea of a bubble sort, or a technique for identifying faces in an image. You cant stop someone else seeing the concept and figuring out their own way to do it, on their own clock, to compete with yours. You can only copyright Postgresql, Sony Vegas, or gzip, if you created those, or your specific code for a bubble sort or face ID.