There appears to be a major question if the Kaddish before Shmoneh Esrei is a preface to Tefillah or is associated with the Ashrei or berachos that precede it.
To satisfy all opinions one should not be mafsik before or after.
See mishna berurah 25:59 that this is apparently a machlokes between magen Avraham who holds to remove tefillin after kaddish and eliyah rabba who holds that is a hefsek
Discussion and Sources
Rambam (seder Hatefila pg 329 Frankel edition) writes that Kaddish is said before and after each Tefilah. Rabbenu Manoach (Hilchos Tefila 9:1 s.v. umaschil) writes that since Kaddish is a short tefilah that discusses the geulah Chazal wanted to prevent us from losing hope of the final redemption from the long and arduous galus that we are in. This opinion is echoed by Rabenu Avraham ben haRambam (sefer HaMaspik 200-1) and others.
However, Shibolei Haleket 8 and Rav Av Bais Din and Darkei Moshe (54) write that the Kaddish is associated with what precedes it. (see Rambam Hilchos Tefilah 9:1, Mekoros vetziyunim, Frankel edition)
Most Kaddish is said it is said after some other item. For example, Kaddish is said after Torah learning (kaddish deRabanan) or after krias Hatorah or after tefillah or after pesukei dezimra, etc. (Mishna Berurah 55:22)
The clearer problem with hefsek would be between the Torah / Ashrei and Tehillim for returning Torah and the Kaddish that follows it. (That is why in some shuls when someone says Birchas Hagomel as the last aliyah, instead of making the beracha before Kaddish, it is said after Kaddish to eliminate the hefsek.)
Having a break in the davening before Kaddish that precedes Musaf is something to avoid. There is some discussion about whether a rabbi's sermon is a hefsek.