Bash – locally created alias not being used if called using backticks (`)

You could use a function in bash (or any POSIX shell) like this:

grep() { 
    if [ -t 1 ] && [ -t 0 ]; then 
        command grep -n "$@"
    else 
        command grep "$@"
    fi
}

The [ -t 1 ] part uses the [ command (also known as test) to check if stdout is associated with a tty.

The [ -t 0 ] checks standard input, as well, since you specified to only add line numbers if grep is the only command in the pipeline.

Simply don't use aliases in scripts. It makes little sense to use a feature designed for interactive use in scripts. Instead, use functions:

somecommand () {
    ls -alF
}

Functions are much more flexible than aliases. The following would overload the usual ls with a version that always does ls -F (arguments are passed in $@, including any flags that you use), pretty much as the alias alias ls="ls -F" would do:

ls () {
    command ls -F "$@"
}

The command here prevents the shell from going into an infinite recursion, which it would otherwise do since the function is also called ls.

An alias would never be able to do something like this:

select_edit () (
    dir=${1:-.}
    if [ ! -d "$dir" ]; then
        echo 'Not a directory' >&2
        return 1
    fi
    shopt -s dotglob nullglob
    set --
    for name in "$dir"/*; do
        [ -f "$name" ] && set -- "$@" "$name"
    done
    select file in "$@"; do
        "${EDITOR:-vi}" "$file"
        break
    done
)

This creates the function select_edit which takes directory as an argument and asks the user to pick a file in that directory. The picked file will be opened in an editor for editing.

The bash manual contains the statement

For almost every purpose, aliases are superseded by shell functions.