Can I access my Android through ADB if the phone can only get to the fastboot menu?
No you can't access your phone via adb while you are in fastboot menu.

While in fastboot menu only the fastboot binary + driver can access your device. 

ADB is only available when the device is booted (adb is usually already available from a certain boot stage on while the device is still booting). 

Also certain recovery ROMs provide full ADB access. Simple recovery ROMS only provide limited ADB access, for adb sideload - it allows you to upload ROM images so that the recovery can install it.