Damaged Home Button

It would be a different repair than that of the screen.

Ref: iPhone Repair - Official Apple Support

Other iPhone repairs

Do you need a repair for other issues like the Home button or liquid damage?

• If your iPhone issue is covered by the Apple warranty, AppleCare+, or consumer law, there's no charge. This does not include accidental damage, which requires a fee.
• If your iPhone was damaged and you have AppleCare+, the coverage includes accidental damage protection. Each incident has a service fee.
• If your iPhone was damaged and you don't have AppleCare+, your repair fee will vary, depending on the repair. The out-of-warranty prices on this page are for repairs made by Apple. Apple Authorized Service Providers may set their own fees.    

Not sure if you're covered? Check if you have AppleCare+ coverage by entering your iPhone serial number. 

Learn more about AppleCare+ for iPhone

Sounds like a good deal. The bottom line is that the Apple technician has the responsibility to evaluate the phone and sets the resultant repair costs estimate. You then have the option to proceed with the repair or not.

Apple only does customer repairs as complete replacements of the entire front screen assembly, including the home button if included. So if there's any damage to the assembly including glass breakage, display malfunction, or the home button/Touch ID then any combination would be fixed as a single replacement.

That doesn't mean that they might not replace the home button for later use as a refurbished front screen assembly. Replacement parts can be refurbished.

They could have different rules for AppleCare+. Certainly if the home button was in working condition but the glass was cracked, the home button could potentially be reused to create new replacement front screen assemblies.. However, you're probably better off taking it to an Apple Store (if available) to see what they say. They could have a different answer than phone support.

I do know that if somehow the front screen was damaged including the home button and I was paying out of pocket for it, that would just be Apple's flat rate cost.