Yes, it is possible, but the boot time will be increased. The easiest way is to create a Windows 95 OSR2+ or 98 floppy startup disk and make the changes to the content afterwards.

BTW, there are troublesome DOS games that requires MS-DOS mode from the late 90s too: Crusader series and Alien Trilogy.

i have a win98se boot floppy for a win95 rtm system just so i can access a fat32 extended partition on a rather large cf card that would just be too cluttered with 2gb fat16 partitions. not everything has to fit on the floppy. if the floppy is specifically for this system you can just reference drivers and programs on the c: drive from the floppy config.sys.

Agree with stanwebber your much better off putting the drivers, etc on c:\ and have the boot disk reference them.

From a dos prompt you can either type
format a: /q /s (this will wipe the disk and make it bootable
or
sys c: a: (this will make the floppy bootable without wiping the disk)

I think this still worked in WinME? if not you can boot from a Win98 CD which will temporally give you Win98 based system

Make a backup of config.sys and autoexec.bat if they exist on c:\ (as it looks like Phils installer overrides them)
Run Phils installer as per normal
Copy the autoexec.bat and config sys files over to a:\

and you should be good to go, boot time should be pretty close to booting off the HDD as it'll need to access the FDD much less.

I think that another option is to create a boot floppy image (or small hard disk image) and then install a boot loader which can boot from images. I've done this kind of thing with SYSLINUX but not in your particular setup with Windows 9x/Me.

The drawbacks are that the entire disk image is kept somewhere in RAM (not in the first 1MiB though), I think one to a few KiB are used for what is essentially a driver that allows DOS to see the virtual disk, and I suspect if you tried to run Windows 9x off the disk image it would not be happy that it can't do 32-bit disk access.

The main benefit is you don't need to actually insert/remove a floppy disk. Instead you just get a boot menu, and it's easy to have multiple options because you can make multiple disk images. Another benefit is that it's configured much like PXELINUX so if you learn how to do this you can also set something similar up for booting over the network from another machine. Also you can make graphical menus if you like, I've never tried it but many Linux live CDs use ISOLINUX which another member of this boot loader family, so you may have seen these before.

If anyone is interested I can write something up about this.

besides sys/isolinux i have used grub4dos to boot image files from a dual boot xp/98se system. i chainloaded it from the windows nt bootloader, but i understand it is a standalone boot manager in its own right.

i always wondered if this is better

http://digitalarcane.blogspot.com/2015/01/

that blog shows screens of how it looks
there are many versions over the years since they even released some that work on windows XP