The problem you are having with multiple lines was caused by defining your file as only containing a single line. Here's what you need:
:default ::= action => [values]
:start ::= Definitions
:discard ~ ws
Definitions ::= Definition +
Definition ::= Alias <new line>
As for the backslash'd newlines, to treat them as horizontal space, you want something like:
ws ~ <ws element> +
<ws element> ~ [\s]
<ws element> ~ backslash [\n]
<backslash> ~ '\'
I did test both of these with your multi-line example and they seem to work. The Sudoer's format is newline-sensitive -- it treats horizontal and vertical whitespace differently. You'll probably need to nail down exactly where newlines are OK according to the spec, before you're 100% compliant. Marpa has a mailing list, btw, where expert users hang out. Several of the people on the group have more experience with parsers for this kind of file than I have. You might consider joining up.
I hope this helps.