Not exactly. UCSD does direct admission to most engineering majors (see exception below), but may admit students rejected from the major to an alternate major or undeclared. Because the only space available for current students wanting to change major to an engineering major comes from attrition (which is low at a school as selective at UCSD), changing into an engineering major after enrolling at UCSD is very difficult – generally more difficult than at schools where all engineering students are admitted to pre-engineering and must compete for the total number of available space in engineering majors. See https://www.ucsd.edu/catalog/curric/SOE.html . Some other schools, like UIUC, have similar systems.
At UCSD, one engineering major, engineering physics, admits to a pre-major status, where all students must compete for the spaces in the major in college, similar to how Texas A&M, Purdue, Minnesota, Virginia Tech, etc. handle their engineering enrollment.