May one ever make an interruption between Geula and Tefila?
The Gemara (Berachot 42a) explains that there is great importance to juxtapose “redemption” with “prayer”. What this means practically is that the blessing of “Ga’al Israel” -which discusses Hashem as Redeemer of the Jewish people- should be immediately followed by the Amida, which is the core of prayer. Furthermore, the Shulhan Aruch (Orah Haim, 111:1) says that because this juxtaposition is so important, no interruption is permitted between the two. Although the introductory verse (Tehilim 51:17) “Hashem Sefatai Tiftah…” would appear to be an interruption, practically speaking it is part of the Amida and is thus permitted. Not only is a verbal interruption not allowed but even a pause longer than the time it takes to greet one’s rabbi (“Shalom Alecha Rabbi”) is considered an interruption. Therefore, as soon as one recites “Ga’al Israel” one should immediately start the Amida with “Hashem Sefatai Tiftah”.
The Rama (ibid.) posits that this uninterrupted juxtaposition is crucial specifically on weekdays and on holidays but not on Shabbat. His rationale is based on the last verse of Tehilim 19, which discusses Hashem as Redeemer, and is immediately followed by the first verse of Tehilim 20, which says that Hashem will answer those in distress. Since Shabbat is not considered a day of distress, then Redemption need not be followed by Prayer, and one would be able to reply to Kaddish, Barechu, etc. (Although Yom Tov has an element of joy, they are considered days of judgment, and thus the aforementioned verses would apply just as on weekday). The Yalkut Yosef (111:5) rules accordingly and says that if one were to hear Kaddish or Barechu, for example, in beween “Ga’al Israel” and the Amida, one would be able to respond on Shabbat. That being said, the Shulhan Aruch makes no distinction between Shabbat and other days, and the Ben Ish Hai (Year II, Parashat Toledot) says that this is the custom. The Siddur Bet Oved (Hilchot Tefila), based on the Kaf Hahaim (K.H., O.H. 111:8), says that even if one only had access to Tefilin right between “Ga’al Israel” and the Amida, one would be permitted to don them but not to recite their blessing.
Interestingly, there is an Ashkenazic custom for the Shaliah Tzibur to lower his voice in the latter half of the blessing when saying the words “Ga’al Israel” in order to prevent anyone from accidentally responding to the blessing had they heard it out loud. The Moroccan and Sephardic custom, however, is for the Shaliah Tzibur to say it at regular volume. Indeed, there is a custom to say the first word of the Amida out loud right after the blessing (“Baruch Ata Hashem Ga’al Israel-Hashem…”) to show that no interruption is being made in between.
Summary: One may not make any interruption between the blessing of “Ga’al Israel” and the Amida.