It can matter, depending on what GPA or other criteria are needed to enter the major.
https://www.engr.washington.edu/current/admissions/admitstats (competitive, average GPA of ME admits is 3.6; essay required when applying to major)
https://advising.engineering.osu.edu/current-students/applying-your-major (3.4 prerequisite GPA to guarantee admission to ME, otherwise competitive)