Does the attribute of omnipresence apply to the earthly life of the Lord Jesus?

This text is from a transcript of a talk by David Gooding, entitled ‘What it Means to be a Believer’ (1989).

The answer to that and similar questions has exercised the biggest Christian brains in Europe for centuries. What I can say about it in only a brief time I really do not know. I do find it helpful, however, in my own thinking, to always remember that while Jesus Christ our Lord was truly and perfectly and completely human, he who was incarnate in Jesus Christ was nothing less than infinite God. There is necessarily a mystery about the person of our Lord, as he himself observed, that only God can and does understand. 'No one knows the Son save the Father' (Matthew 11:27), and here as we contemplate such a mystery, the proper attitude is one of worship more than analysis.

We must be careful how we speak of the Lord Jesus and what kind of rational deductions we make. He is God incarnate, but you would be wrong if you were to say, as the Old Testament does, 'Well God never slumbers or sleeps,' and then proceed to deduce that because Jesus Christ is God incarnate, he never slumbered or slept. He fell asleep in the boat (Luke 8:23). He was truly human but as far as I understand it, while our Lord was truly human, he was not merely human. He was the Word incarnate and the Word was always omnipresent and never ceased to be anything else. There's no record that the body of our gracious Lord was omnipresent, but when we talk of omnipresence, we're not tied to physical things. I simply repeat that our Lord was truly human. His body knew the limitations of our time and space, our hunger and cold, our heat and pain, and our sorrow and weakness; though not sin. But the one who was incarnate in Jesus Christ was God overall, blessed forevermore.