Yes, I think engineers do use the results from his paper to design algorithms behind the hardware of medical imaging, there are like bazillions of 'l1 recovery sparse signal', 'sparse approximation', 'compressive sampling' type algorithms in the years following that publication until today. No, they are not tinkering around randomly when they write the programs from those algorithms.
from cursory googlinghttps://people.eecs.berkeley.edu/~mlustig/CS/CSMRI.pdfhttps://authors.library.caltech.edu/10092/1/CANieeespm08.pdf
I don't know if the engineers can derive results such as Restricted isometry https://en.wikipedia.org/wiki/Restricted_isometry_property
or the robust uncertainty principles and all the bounds involved, but I know that this paper https://arxiv.org/pdf/math/0409186.pdf
shows there is a way to get around the fundamental limitation of Nyquist Shannon sampling theorem and thus created a new paradigm for signal processing.
I think the main reason people think Tao is a meme is because he gained a lot of fame without being a theory builder, i.e he didn't create any theory so that lay people can quote and go 'woo wee' but he's more of a problem solver, he solves specific technical problems that are incomprehensible to non experts, so it's a reasonable question to ask how come this guy is famous, what has he done. The answer is nothing you could appreciate unless you spent years studying the relevant research literature.>>11384686
You can just ignore those articles that has low citation or too high ratio of self citation, I'm not even looking at them. There are ridiculously many papers cited by people from different fields it's actually hard to keep track of.