May one answer Amen Yihei Shmei Raba for Kaddish in middle of the blessing of Yishtabach?
No. Once one has begun the words of Baruch Ata Hashem in the conclusion of the blessing, one may no longer answer for a regular Amen. However, it is disputed amongst the Poskim as to whether it carries the same law as Baruch Sheamar, which itself follows the same law as the Shema, in which we rule that one may answer for Amen Yihei Shmei Raba, and Deamiran Bealma. Practically, one is to avoid the dispute by either waiting prior to the blessing once Kaddish is begun, or by quickly finishing the blessing so one can answer. If one could not do so then he is not answer for any Amen, as rules the stringent opinion and as is the implied opinion of Admur.
Explanation: By Baruch Sheamar after the blessing has been started, the ruling is that one may answer for all Amens permitted to be answered in middle of Shema, as although one is technically in middle of a blessing, since it is a long blessing therefore we are lenient to permit answering for certain Devarim Shebikidusha. Now, the question is asked as to how we should relate to the blessing of Yishtabach which is much shorter than the blessing Baruch Sheamar. Do we view it as a short blessing in which one may not answer for anything, or do we view it as a long blessing in which case it follows the same law as Baruch Sheamar. Practically, this matter is debated amongst the Poskim, and hence we concluded as above. As for the opinion of Admur, it is implied from the wording of Admur in his Shulchan Aruch that one may not answer for anything in middle of the blessing of Yishtabach, and so rules the Ketzos Hashulchan, and hence certainly one should not be lenient in his opinion, as is printed in the Luchos of many Chabad Siddurim [unlike the Luach of Rav Lemberg, who rules as the lenient opinion]. This is all in addition to the fact that according to Kabbalah, as recorded in the Poskim, that a person is to be very careful not to make an interval between the 15 praises which are recited in Yishtabach [starting from the words Shir Ushvacha ], and is to say them from beginning to end without stopping in-between and that if one is not careful in this there is danger involved.
Sources: See regarding Baruch Sheamar: Admur 51:3 and 5; M”A 51:3; Tehila Ledavid 51:1; Kaf Hachaim 51:11; Ketzos Hashulchan 18:2; Piskeiy Teshuvos 51:4; 54:2 Poskim who are stringent: Implication of Admur 51:5; M”B 54:3 leaves in question; Ketzos Hashulchan 18:2 footnote 5; Piskeiy Teshuvos 54:2 Luchos printed in certain Tehilos Hashem Siddurim; Poskim who are lenient: Chesed Lealafim 54:2; Derech Hachaim 30; M”B 51:2 in name of M”A [see however M”B 54:3]; Siddur Yaavetz; Kitzur SHU”A; Kaf Hachaim 53:2; 54:7; Dinei Hefsek Betifila Chapter 3 footnote 4 and in his Luach in back [no mention is made of the Ketzos Hashulchan above]