MB 11: he shouldn't stop - and the later authorities wrote that during Baruch she'amar, Yishtabach, and the Verses of Praise one should stop in order to accept the yoke of heaven with the congregation, but during the blessings of Shema and even between the blessings one shouldn't stop at all, but rather should say the words of the blessing in the tune that the congregation is saying Shema.
Avi Bloch
sha-65.03
Siman 65. One who comes to Shul (Synagogue) and finds the congregation reading the Shema, or one who interrupts while reading (cont.)
65:3. If after reading the Shema, one entered the synagogue and found the congregation reading the Shema, then it is good if he reads the whole of it with them - and he will receive reward as one who is reading Torah [as he has already fulfilled his Mitzvah of reading the Shema before coming into the synagogue, he has already merited the reward for that --SP]. {Rema: But he is only duty bound to read the first verse [with the congregation] as we have explained [in 65:2].