"Секси" is a relatively new development (a matter of years, not decades). You won't see it in any serious dictionary, because it's kind of slang, and not an "official" Russian word. I can't think of any truly Russian indeclinable adjectives.
Personally I do not use "секси", ever, it's too ... lightweight.Some people are too self-conscious (or too lazy) to say "сексуальный" or "сексапильный", which means that you really talk about sex and sexual appeal. When you say "секси" it's something to fill the pause in girlish gossip and it does not mean anything, except that the guy is a cutie.
I think that "секс" and "сексапильный" was borrowed from French, but I'm not sure. The word "секс" was used in Russian for a loong time, but it had either negative or medical connotations. Nice people did not "занимались сексом", they "занимались любовью". )))Finally, are there any Russian words for sex that are more native than this? Surely you Russians had some words for sex before you stole them from english...
Among Russian analogues there are a very formal "половая жизнь" (= sex life), a very old-fashioned "плотские утехи/плотские наслаждения" and a neutral "спать с" (to sleep with). There are a rather rude slang word "трахаться" (to have sex) and a well-known "е@%ться" from Russian mat. Hmm.. Anything else?