A similar question is also discussed in the context of the night time kiddush where many people have the custom to begin with the word "yom hashishi", which is also the last two words of a pasuk, without quoting the entire pasuk. The Chosam Sofer (Orach Chayim 10, 4th paragraph here) discussed this particular example, mentioning that some forbid this practice. He himself allows it, because (in short) the recitation of this half-verse is not meant to be a recitation of a verse, but merely an introductory phrase.
This line of reasoning is followed by his student, the Maharim Shik (Teshuvah 124), where he applies this same line of reasoning to the question at hand regarding 'al kein' before the day kiddush. He states that the phrase is merely a declaration of the sanctity of Shabbos, and 'בדרך צחות', as a way to be sharp, we use the biblical phraseology, but we are not reciting a verse qua verse. Similarly, the Aroch Hashulchan (O.C. 289:3) also allows this practice of starting with 'al kein', for the same reason: because the intent is not to state a verse qua verse, but merely to say a nice thing about Shabbos, there is no problem of splitting pesukim. This is also allowed by the Ben Ish Hai in Shu"t Rav Pealim (1:11) where he explains in detail all of the places where we seem to split pesukim in our liturgy.
Despite all of the above, the Mishnah Berurah (289:2) prohibits saying this partial verse without saying the full verse (he does not quote a source for this stringency in the Shaar Hatziyun).