Power button no longer turns screen on/off - apps don't fix this properly, cannot turn off phone to root it, help!
Most likely not. The bootloader should typically issue the standard reboot bootloader command. However, in case of Samsung, the command needs to specify the reboot download instead. An XDA thread mentions that the following adb command brings to the download mode - adb reboot download. Maybe you can use that instead?

As per this answer, Samsung phones do not support Fastboot mode. Most of the times you'd be living off ODIN, but can also use heimdall. Don't forget to follow its commands cheatsheet as it does seem to not support the standard fastboot commands. 

Also, I just wanted to remind you that if you are able to reboot the device with the Power + Volume Down combo, the same should also work when you shut down the phone but then fail to turn it back on.