Order of adjective and noun
Placing adjective before the noun, like '奢侈品' is a normal grammar structure, you cannot go wrong with that

When you put an adjective after a noun, the noun is acting as the topic, and the adjective is acting as a comment. 

他的生活奢侈 

他的生活 (his life) is the topic

很奢侈 (is luxury) is the comment, 

you can replace 'is luxury' with other adjective (comment), for example '艰难' --> "他的生活艰难" (his life is difficult)

Not all noun can be a topic, especially a single character noun like 品. 

Not all adjective can be a comment

For example: 

'这家公司的发展非常迅速' make sense;  

'这家公司的发展非常海外' doesn't make sense, 

although '海外'  is a legit adjective for '发展' as in '这家公司的海外发展'

Without clear context, 生活奢侈 can also be interpreted as a [verb + adverb] structure, with 生活 as a verb, and 奢侈 as an adverb. That's why I add a subject and possessive 的 to clarify '(他的)生活' is a noun