As some comments indicate, omitting the preposition in constructions of the basic form "X looks [like] Y" (where X is a noun, not an adjective) seems to be less acceptable in AmE than BrE.
As a Brit, I have no problem with OP's example. In his 1951 novel The Masters, the English chemist and novelist C P Snow wrote...
At a first glance, people might think he looked a senator.
Since C P Snow would definitely be considered a competent writer, I think we can dismiss concerns that the usage is "ungrammatical" in any meaningful sense. And leafing through the results in Google Books for "looks a safe bet" I see several that are unquestionably AmE sources. For example, this is from an American book about baseball...
...it looks a safe bet that Comiskey will have a regular soldier drilling the Sox at their Texas camp.
Comparing US/UK corpuses in Google NGrams for to look a picture, I can't see much evidence of a usage split. And Google Books claims 89 instances of "You do look a picture" (I included do to ensure most/all instances were relevant to the usage under consideration), but there are no written instances at all of "You do look like a picture".
TL;DR: You will encounter some native speakers (particularly, Americans) who have misgivings about the usage in general. But I think even many of those people would be more accepting of my safe bet/picture examples than they would of OP's particular version. It's more a matter of what you're used to hearing, rather than a specific point of "questionable" grammar.