Note: The explanations that I give below may not contain 100% correct information about the operation of hardware and software, they are based on my personal experience dealing with computers as an end user
Yes, Windows 9x may not be able to read the files on the CD because:
1 - Windows 9x setup does not install any CD-ROM drivers for DOS. The boot floppy loads them to start the setup from the CD-ROM but the setup program needs to reboot the computer and those drivers loaded from the floppy will not be available on the next boot from the hard drive.
2 - Windows 9x setup will disable any CD-ROM drivers for DOS previously installed on the hard drive, it will edit autoexec.bat and add "rem - By Windows Setup -" at the beginning of the line that loads MSCDEX.EXE
And then on some systems with enhanded IDE controllers/chipsets it will be unable to read the CD-ROM until it installs the proper drivers that are stored... in the CD-ROM
Windows 9x will still run from the IDE (or SCSI if the controller card has its own BIOS extensions) hard drive because the BIOS handles that access without MS-DOS needing any additional drivers, and Windows is using the drive in "MS-DOS Compatibility mode" which means calling MS-DOS that is "under the hood" to read from and write to the hard drive(s)
In Windows 9x/ME MS-DOS is always there waiting until any program needs to use some MS-DOS function, that program may be Windows itself if it doesn't have specific drivers for certain hardware.
Windows disables the slower 16-bit drivers in autoexec.bat because the hardware is not able to support the requests of both the 32-bit and 16-bit drivers simultaneously.
If those 16-bit drivers are re-enabled in autoexec.bat Windows will still be able to work (at least in most cases of CD-ROM drivers) but without loading the equivalent 32-bit drivers, so it will work slower or with any other kind of limitations.
If the Setup program is interrupted because it cannot access the CD you can usually use a floppy to reinstall the CD drives for MS-DOS, it may be the Windows 9x floppy itself in which case you have to copy and configure the drivers manually or the floppy supplied with a CD-ROM drive that usually installs and configures everything automatically.
Then you can restart the Windows setup from the Windows CD and usually it will continue where it stopped, but not always, that's why some recommend to copy the setup files to the hard drive and run the setup from there.
The Windows ME setup already does that automatically, at least if there is enough free disc space.