In responding to my own question, it is possible with some caveats.
If the driver is takes up consumes more RAM that the UNIDIS3C does (4K), you will need emm386.exe and load it from config.sys. An example of this is below. The default BL settings for himem.sys and the commented emm386 will cause problems loading the network TSR programs. The blade.img file isn't large enough for the Windows 98 EMM386. The solution is to create a larger (2.88MB) bootable image file. The mkbt utility from Bart's BOOTCD page can do this using the original blade.img file. Once the image is bootable and filled with the contents of the original blade.img file, it can replace blade.img in %tftproot%\X86PC\pxelinux.
You will need cabarc.exe or some cab creation utility to recreate the net.cab file in blade.img
In the net.cab file:
1) The driver's image name (NAME$) must replace the UNIDIS3C$ entry in the GEN_NDIS stanza of the PROTOCOL.INI file. Any driver settings should also in that stanza as well.
2) The driver filename should replace the UNIDIS3C.DOS entry in the SYSTEM.IN_ and SYSTEM.INI files.
3) Add the new driver file to net.cab
4) Recreate net.cab and put it back into the image.