Not really, because if I recall (it's been nearly a decade since I read it) it isn't about Sirk's life or career and it doesn't analyze the films in great detail. It's about how Sirk's 1950s Universal melodramas have been received in a variety of contexts--from their original popular reception to their uses in film criticism and academic film studies. It's an early and exemplary instance of "reception studies," if that sounds interesting to you.Would you recommend Klinger's book as a good introductory text to Sirk?
I would recommend the Jon Halliday Sirk on Sirk volume, which I believe is out of print but can be found. Sirk is a fascinating guy, and it's not an easy book to put down. Halliday was one of the first critics to show such a great interest in his films, and Sirk obviously takes great pleasure in talking to another worldly and sophisticated man about films that had only just begun to be taken seriously by the film intelligentsia. Like I mentioned above, I think it's worthwhile to sometimes read Sirk's responses against the grain. But he hardly spends all the time flattering his interviewer; they have a few very telling disagreements.
Unfortunately there is still no English-language study of Sirk's career (!!), or even one that has a lot of research on his American films' production, style, etc. I've long thought that someone ought to do for Sirk what Lutz Bacher has done for Max Ophuls's American period (Sirk, btw, was a major fan of Ophuls's Hollywood films). There are a ton of articles about Sirk, but I'd have to have a bibliography handy to make recommendations!
First things first though: presuming you've seen the major American films, I would get a hold of, if you can, some of Sirk's German features (esp. Schlußakkord a.k.a. Final Accord, Zu neuen Ufern, and La Habanera.) Both the continuities and the differences between those films and his later American films are very instructive.