gistfile1.txt

$ cat inventory
---
all:
  children:
    my_poc_hosts:
      hosts:
        target1:
        target2:
        target3:
  
# Undefined for hosts if no user given  
$ $ ansible -i inventory all -m debug -a var=ansible_user
target1 | SUCCESS => {
    "ansible_user": "VARIABLE IS NOT DEFINED!"
}
target2 | SUCCESS => {
    "ansible_user": "VARIABLE IS NOT DEFINED!"
}
target3 | SUCCESS => {
    "ansible_user": "VARIABLE IS NOT DEFINED!"
}

# Defined by default for locahost on local connection
$ ansible -i inventory localhost -m debug -a var=ansible_user
localhost | SUCCESS => {
    "ansible_user": "my_user_obfuscated"
}

# Defined for hosts if given on command line
$ ansible -i inventory all -u toto -m debug -a var=ansible_user
target1 | SUCCESS => {
    "ansible_user": "toto"
}
target2 | SUCCESS => {
    "ansible_user": "toto"
}
target3 | SUCCESS => {
    "ansible_user": "toto"
}

# .... and ok also with ask-pass ask-sudo-pass
$ ansible -i inventory all -kKu toto -m debug -a var=ansible_user
SSH password: 
BECOME password[defaults to SSH password]: 
target1 | SUCCESS => {
    "ansible_user": "toto"
}
target2 | SUCCESS => {
    "ansible_user": "toto"
}
target3 | SUCCESS => {
    "ansible_user": "toto"
}

# Does not change for local connection even if you specify a different one
# Defined by default for locahost on local connection
$ ansible -i inventory localhost -m debug -u toto -a var=ansible_user
localhost | SUCCESS => {
    "ansible_user": "my_user_obfuscated"
}