You can not boot PXE without entering the password.
It may be possible depending on the manufacturer but the majority won't be able to boot to the PXE without the password.
You can't boot to the PXE because the BIOS has to initialize before it can boot and one of the steps in the initialization process is the password check. After the password has been supplied it will continue through its initialization. After it has finished it will boot from the top device in its boot priority list. If that happens to be PXE then it will boot to PXE. Because PXE is Generally not part of the BIOS initialization, you won't be able to "Auto-enter" the password.
PXE is actually part of your network controller/card. You can compare it to the custom RAID firmware some add in cards have.
There may be proprietary approaches to counter this issue such as not requiring the password when the computer is Waked-On-LAN. I personally don't have a computer that will bypass the password but I do have one that if it is waked on lan it will automatically do a PXE boot (this behaviour is configurable).
Hope that I was able to help!