As per the philosophy of Bhagwat Gita & Hinduism, God is omnipresent (present everywhere) in it's un-manifest aspect & is always present all around us. Every inch of the space is occupied by Him. Every nook & corner is filled by Him. In this aspect He is called Brahm (God) who is Truth Absolute, Knowledge Absolute and is Infinite.
It is this un-manifest aspect of God that is present in Clay Idols that Hindus worship as their God. Now to fulfill the desire of a devotee, this un-manifest, all pervasive Brahm (God) who is there in Clay Idol, by the power of His Yogmaya, manifests Himself as an embodied Being and appears before the devotee. So in this way the Un-manifest God in Clay Idol becomes manifest before the devotees.
So this omnipresent, un-manifest God appears before a devotee in whatever form he worships Him, whether it is the form of Rama, Krishna, Vishnu, Shiva, Shakti, Ganesha or any other form. A devotee should always remember that the God whom he worships, always pervades through this whole universe & can manifest Himself in any form, anytime He wants to appear before his devotee. God is never invisible to such souls who have understood His true nature, nor does He ever lose sight of them.
In Bhagwat Gita, Arjuna asked Lord Krishna to show him the "Cosmic Form of God" & Lord Krishna showed Arjuna his physical "Virat Rupa" or "Cosmic Form of God" in which all these universes & all these planets, stars etc. were present. This physical "Virat Rupa" of God or this whole universe is the external body of the omnipresent, un-manifest God. Similarly this small Clay Body of God is the miniature aspect of that "Virat Rupa" or all inclusive physical universes.
Generally we see that, whenever, people go to the temple & come in front of the Clay Idol, people close their eyes. Why it is so that when people come before their revered God, they close their eyes? Simple answer to this is that they feel God much closer to their heart inside themselves when they come in front of the Clay Idol. Yes, God who is there in omnipresent, un-manifest aspect in the Clay Idol is also sitting in their hearts in un-manifest aspect. So that is the reason that while closing their eyes before the Clay Idol, people feel the presence of un-manifest God present everywhere & also in their heart.
So the answer to the question, "Whether God is actually there in the Clay Idol or not?" is in Yes. Yes, God is there in the Clay Idol. Let us respect the feelings & thinking of those people who do Idol Worship.