Q. If one in the middle of Shemonesrei hears the laud answering by the congregation of the 13 Middos, should he momentarily stop his recitation and have in his mind answering with them as one is supposed to do when hearing Kaddish or Keddusha?
A. Betzel Hachochmo (5: 61) rules that when one is in the middle of reading the Shema or it’s brochos, he does not stop to answer the 13 Middos, and certainly in the middle of the amida he does not need to stop and have intention to answer in his mind. (Ratz Katzvi 4: 9). Igrois Moishe (O.H. 3: 83) that a Torah shiur attendants do not have to stop their learning to recite the thirteen middos together with the minyan. (See also questions 603 and 1796).
Horav Shlomo Mille’s Shlit’a opinion is similar.
Rabbi A. Bartfeld as advised by Horav Shlomo Miller and Horav Aharon Miller Shlit’a