Critical path can move if certain variables are changed or solved, yes.

Often in multi-disciplinary fields there is a firm critical path that doesn't change much (e.g. "we gotta build this custom mechanical thing that only this Swiss firm seems to know how to build vs all the easier software and electrical and IT details we can do in-house".

But if initial assessments are wrong "hey, it turns out this other firm already has the thing we need to build" or "wow it turns out this software detail is 10x harder than we thought" then the critical path can change.