The short answer is, “no”. Another short answer is that I don’t know of any classical theist who held that God is distant and doesn’t care about what’s happening in the world. In fact, such a conception of God would be that of deism, not classical theism and thus guilty of being a strawman objection.
When one thinks about the concept of God in classical theism, it’s impossible for Him to not be personal, present, involved, and so on.
Since God is Omnipotent and Omniscient, it follows that God is Omnipresent. Since God is Omnipresent, He is thus Immanent in the world.
Also, Classical theists affirm that God is Omnibenevolent. From this, it follows that God is Love and thus Gracious.
Therefore, Classical theists affirm that God is Omnipresent, Immanent, Love, and Gracious. This is a far cry from being “impersonal, not caring, not loving, and not involved”.
But how can God be Immanent and yet Transcendent? (outside of space and time)
God can be both in virtue of what it means for God to be immanent. God being involved is in virtue of Him knowing all true propositions in conjunction with Him being all-powerful. The better objection would be, “How can God be Transcendent and Everlasting?”. I don’t really think He can, unless you qualify it by saying, for example, that God is Transcendent without creation and Everlasting with creation.