As some one from Asia, and idol worship is common, I would say, yes, there is demonic power in these objects, whether the bearer believes it or not.
But even if you disagree with me, this is what the Bible says regarding this:
1 Corinthians 10:19-21 What say I then? that the idol is any thing, or that which is offered in sacrifice to idols is any thing? But I say, that the things which the Gentiles sacrifice, they sacrifice to devils, and not to God: and I would not that ye should have fellowship with devils. Ye cannot drink the cup of the Lord, and the cup of devils: ye cannot be partakers of the Lord's table, and of the table of devils.
Yes, food being offered to idols is a very practical lesson on what to do for us in Singapore, you know, because this kind of thing really happens. Is it the same for you? Would you take the Word of God and apply it? What if you go to a friend's house when they are serving food that you know not if the food had been offered to an idol before hand? (But there is a huge idol sitting in the living room of the house?)
There is a power behind these idols and that is the devils'. From what I gather from reading here, I find many "western" (as opposed to "eastern or asian") posters dismiss these as something akin to "hocus pocus" . THat's ignorance to the spiritual battle that is raging in the heavenlies and the Enemy can have free discourse because of this ignorance.
blessings and peace to you.