NOT A TEACHER
No, you couldn't – the two have different meanings.
In this context, 'luxury' has a particular meaning: the best, the most expensive, the most prestigious. A brand that you would expect rich people, and maybe even famous people, to buy.
'Luxurious' appears to have a similar meaning, as in very comfortable, very expensive. But it is applied to a particular class of things – you would mainly describe soft things as being luxurious. It could be thick towels, fur coats, cosmetics, the feeling of the bubbles made by washing-up liquid (if you are an advertiser!)...but not shoes, and not a brand of anything.
Hope that helps!