Reagan was 100% a true believer. It was not cynical on his part. He believed it would work, he believed it was the moral answer to the nuclear problem, he believed (however naively) that one could even share the technology with the USSR eventually, to create a nuclear-free world. His enthusiasm in the technical aspects came from both a faith that American science could solve any technological problem if given enough support (a common-enough attitude of someone of his generation, and even today), and because he had been swayed by the hyperbolic claims of Edward Teller and his co-workers that, it was later revealed, dramatically understated the difficulties and overstated the successes. But the latter was also a case of Reagan choosing to believe what he wanted to believe on it (again, a fairly common political malady).

I would not call it a "mad claim" but it was definitely a claim that went in the face of much technical evidence and much political sense (as Gorbachev noted at Reykjavík, the USA had milking technology under export control to the USSR, they weren't going to share space laser tech). For Reagan it was more of a moral goal than a political one, which is what made his adherence to it, in the face of considerable political opportunity and technical problems, look so "mad." You can think of it as Reagan's personal response to the threat of nuclear annihilation — an attempt to make nuclear weapons a non-issue and non-threat in the world (albeit one that, from the Soviet perspective, was also consistent with the technology you'd need if you wanted to destroy another nuclear-armed nation in a "first strike" attack).

William Broad's Teller's War, and David Hoffman's The Dead Hand, both cover Reagan's views on SDI well.