Halacha forbids studying Torah in the morning before reciting Birkot Ha'Torah. Does this apply to verses that one recites as prayer, and not for the purpose of study?
One example is the Selihot service, which we recite in the morning during the month of Elul, and between Rosh Hashanah and Yom Kippur. The Selihot prayers include numerous verses, but these are recited not for the sake of Torah learning, but as part of our supplications to G-d. Another example is the "Va'titpalel Hanna" text that many have the practice of reciting before Shaharit in the morning, which contains verses from the Nebi'im (Prophets). Are these recitations permissible before one recites Birkat Ha'Torah in the morning?
This issue is subject to a dispute among the Rishonim. Several Rishonim – including the Agur, the Maharam Me'Rutenberg, the Maharil, and the Shiboleh Ha'leket – ruled that verses recited as prayer do not require Birkot Ha'Torah. Others – including the Ra'abad, the Tur and the Orhot Haim – maintained that one may not recite verses before Birkot Ha'Torah, regardless of the purpose of the recitation.
The Shulhan Aruch (Orah Haim 46:9) brings both opinions, and then concludes that one should follow the stringent view, and recite Birkot Ha'Torah before reciting prayers that contain verses.
At first glance, it appears that the Shulhan Aruch conclusively sided with the stringent opinion. However, the Hikreh Leb (Rav Rafael Yosef Hazan, 1741-1820) understood that the Shulhan Aruch actually accepted the lenient view, and his intention was that those who wish to be particularly scrupulous should satisfy the stringent opinion. This is how the Aruch Ha'shulhan (Rav Yechiel Michel Epstein, Nevardok, 1829-1908) read the Shulhan Aruch's comments, as well. By contrast, the Hida (Rav Haim Yosef David Azulai, 1724-1806) understood the Shulhan Aruch as definitively ruling in accordance with the stringent opinion.
Hacham Ovadia Yosef draws our attention to a responsum written by the Rambam, and published in his collection of responsa entitled Pe'er Ha'dor, in which the Rambam rules explicitly that one may not recite verses as prayer before reciting Birkot Ha'Torah. Now Rav Yosef Karo – author of the Shulhan Aruch – did not have access to this collection of the Rambam's responsa, and was thus unaware of the Rambam's ruling on this subject. Hacham Ovadia writes that as the Shulhan Aruch generally follows the Rambam's rulings, we may assume that if the Shulhan Aruch had seen this responsum, he would have written decisively that one may not recite verses as prayer before Birkot Ha'Torah, in accordance with the Rambam's position, without any ambiguity.
Therefore, in light of this presumption, Hacham Ovadia concluded that one should preferably be stringent in this regard, and ensure to first recite Birkot Ha'Torah (followed by the customary reading of Birkat Kohanim) before reciting prayers containing verses.
If somebody hears the recitation of Nakdishach before he recited Birkot Ha'Torah – such as if he arrived early for his Minyan and an earlier Minyan is in progress – he may join the congregation's first three responses. Meaning, he can recite the sentence of "Nakdishach" – which in any event is not a verse, but rather an introduction – and then the next two verses, which comprise the essence of Nakdishach: "Kadosh Kadosh…" and "Baruch Shem Kebod…" He may not participate in the final response – the verse of "Yimloch Hashem Le'olam…" – as this verse is an addition to Nakdishach and not an integral part of the text. The reason, it seems, is that since – as we've seen – different opinions exist as to whether one may recite verses as prayer before Birkot Ha'Torah, one may rely on the lenient view in the interest of fulfilling the Misva of reciting Nakdishach. Although generally it is preferable to satisfy the stringent opinion, and ensure to recite Birkot Ha'Torah before reciting prayers that contain verses, in the case where one hears Nakdishach, he may rely on the lenient view so he can seize the opportunity to recite Nakdishach together with the congregation.
Summary: Different opinions exist as to whether one may recite in the morning prayers that include verses from Tanach – such as Selihot and "Va'titpalel Hanna" – before reciting Birkot Ha'Torah. Therefore, one should preferably act stringently and ensure to recite Birkot Ha'Torah before reciting such prayers. However, if one happens to hear a congregation reciting Nakdishach before he had recited Birkot Ha'Torah, he may join in their responses – with the exception of the final response, "Yimloch," which is not an integral part of Nakdishach.