I am thinking about applying there as a transfer student but I don’t know if the school is worth an application. Admissions is very selective and their engineering programs are not as strong as the best colleges in Colorado and California.
What about Yale appeals to you? How did it end up on your list at all?
Where are you transferring from? Why are you considering transfer?
Just so you know, last year, Yale accepted 27 of 1,254 transfer applications.
Just so you know, in the infamous “Yale report of 1828” Yale argued for studying dead languages rather than creating engineering programs to build a work force to fuel the industrial revolution. Yale is the only school in history to both lose its status as an engineering land grant institution and its ABET engineering accreditation. In 2015, Yale decided that computers were no longer a niche field so they moved the computer science department into the Engineering School and invested some money to start preparing for the 21st century. Hopefully they will be done preparing for the 21st century before the 22nd century arrives. 
Some of the history of Yale engineering is described here (note: ECPD is the predecessor name of ABET):
https://seas.yale.edu/i-am/alumnus/yale-history-blog/post-world-war-ii-era#worldwarii-more
Yale had chemical, electrical, and mechanical engineering with ABET accreditation since 1936, but with a gap from 1965 to 1973 (electrical), 1982 (chemical), or 1985 (mechanical):
https://amspub.abet.org/aps/name-search?searchType=institution&keyword=yale
I would select most of the UCs and both Colorado schools before Yale for engineering.
If Yale is “very selective and their engineering programs are not as strong”, why makes you want to apply?
Agree. The only Ivy engineering I would consider would be Cornell, Pennsylvania and Princeton, in that order. And there are several other engineering schools, mostly public, that I would attend rather than Yale.
Things to think about:
Where are you now? Are you taking engineering pre-req courses?
What is your home state? Are there State U’s that would be cost effective?
How much money do you have to spend?
What is the transfer rate into the new college?
What is your GPA?