Is root@[127.1] a syntactically valid e-mail address?
Why? Why not?
It depends on whether you mean addresses in the header (RFC 5322) or envelope addresses (RFC 5321), and in the latter case, whether you include <>, everything between <> (i.e. the source route), or just Mailbox.
It's valid according to RFC 5322, but RFC 5322 allows loads of fun things like comments! and unicorns! and cake! and ponies!. It's just about possible to parse them using Perl's "regular" expressions: Mail::RFC822::Address.
It's syntactically invalid according to RFC 5321 Section 4.1.3 since the grammar only allows address literals of the form 1.2.3.4 or with a prefix of the form "standard-tag:" (e.g. [IPv6:::1]). I've assumed you meant "Mailbox", i.e. everything between <> but not including the source route.
I'd use the latter definition, since an e-mail address isn't much good if my SMTP server won't accept it. (Yes, this is a bit of a horrible definition, but I don't think the internet will move away from SMTP any time soon.)
(Additionally, there's RFC 5336 a.k.a. "UTF8SMTP". I'm not aware of anyone who uses this.)