Generally speaking yes, but for some reason if you want to ask someone what their hobby is the phrase "Які у вас хобі?" звучить краще, ніж "Які у вас захоплення?". But you can use the verb form of захоплення, namely захоплюватися, to make it more natural: "Чим ви захоплюєтеся?". However, this could be a question either about hobbies or about things you admire.
I assume "хобі" is non-declinable, and that's why it also has "hobbies" as a hint? Can it be "your hobbies," or would that require "ваші"?
I'm still trying to determine whether piguy's question was ever answered or not. :-)
I know that хобi, being a loan word, is indeclinable. But, can you make it plural, and say "Якi вашi хобi," as we do in English: "What are your hobbies"? Or does that simply not occur in Ukrainian, in favor of "Якi у вас хобi?"