The linguistic formulation appears pretty convincing to me as a native speaker living in Italy. The publicist is playing on the term stay and "stare" in IT, it seems and to me there is no reason why not. It is clearer and more English like than many "creative" uses of English terms in IT, like "footing". In short my answer is yes, it is appropriate from my point of view as a native speaker. This is also a reference to Steve Jobs' "Stay Hungry", further qualifying it. As I see it Stay Ready and Keep Ready or Be Ready are all very similar in communicative meaning, outside of specific contexts. There may be some who might disagree. To me this is OK, as you put it.

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Note added at 54 mins (2011-12-20 09:40:48 GMT)
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Yes, even if that is one of the least English like phrases in the list it is in keeping with the pattern and as it differs fro "keep smiling" and refers to a common emoticon, to me, it seems perfectly appropriate in this "marketing" context. It is we, translators, and writers and people like this advertising copywriter who are changing the language as we speak and write. This is only proper and fitting in the globally connected world we live in.