The Bet Yosef cites the famous kabbalist Rav Yosef Gikatilla (Spain, 13th century) as establishing that in the "Yeheh Shemeh Rabba" response to Kaddish, one must not make any interruption between the word "Almaya" and the next word, "Yitbarach." Although it appears that the word "Yitbarach" begins the next sentence, Rav Gikatilla taught that the word "Yitbarach" immediately follows "U'l'olmeh Almaya." Accordingly, the Shulhan Aruch ruled that when responding "Yeheh Shemeh Rabba," one must not stop at the word "Almaya," and should instead continue to "Yitbarach."
On this basis, the Ben Ish Hai (Rav Yosef Haim of Baghdad, 1833-1909), in Od Yosef Hai, ruled that one must ensure not to pause at all between the words "Almaya" and "Yitbarach," even momentarily. However, the Siddur of the Rashash (Rav Shalom Sharabi, Yemen, 1720-1777) instructs that one should specifically make a pause between these words. The Od Yosef Hai writes that common custom does not follow this view, and instead follows the teaching of Rav Yosef Gikatilla. It appears from the Ben Ish Hai that if one asks for guidance, he should be told to make a pause, but those who have the custom not to pause should continue observing this practice.
Elsewhere, the Ben Ish Hai writes that no pause should be made between these words, and this is also the implication of the Shulhan Aruch's ruling. Moreover, this is the universal practice among Sephardim, which should be observed.
Summary: The prevalent custom among Sephardic communities when responding to Kaddish is to recite "Le'alam U'l'olmeh Almaya Yitbarach..." without any pause between "Almaya" and "Yitbarach."