Not one bit.
Just like we say קריאת שמע (preferably with תפילין) in the morning before davening, bentch Lulav & Esrog before davening, so too many blow shofar before davening (especially for families with women and children). After being מקיים the מצות עשה דאורייתא, people do eat. Many people would hold off on the Shofar, as they wanted to be yotze with the Rebbe's תקיעת שופר, but since that is unfortunately not an option now, people do blow Shofar before davening.
In all my years in yeshiva, on bochur shlichus, in a smicha program, and among Chabad communities, I've never seen anyone put on tefilin just to say shma and I've never seen anyone blow shofar in order to eat before davening.
Maybe you do, but clearly those aren't actual minhag chabad for the 99%.