It is very unlikely, but let's begin by examining some Christologies found in Gnosticism:

But the father without birth and without name, perceiving that they would be destroyed, sent his own first-begotten Nous (he it is who is called Christ) ... He appeared, then, on earth as a man, to the nations of these powers, and wrought miracles. Wherefore he did not himself suffer death, but Simon, a certain man of Cyrene, being compelled, bore the cross in his stead; so that this latter being transfigured by him, that he might be thought to be Jesus, was crucified, through ignorance and error, while Jesus himself received the form of Simon, and, standing by, laughed at them.

Irenaeus, Against Heresies 1.24

This passage seems to observe in the Christology of Basilides that Christ was not incarnate as a man, though certainly indicates Christ was divine. We see similar Christological views in Ignatius of Antioch's Letter to the Smyrnaeans, and in 1 and 2 John. All of these individuals arguing against this Christological viewpoint reassert that Christ came in the flesh, and was divine. So, I'd argue that this form of Gnostic Christology influencing proto-orthodox Christology is somewhat unlikely.

The other common form of Christology in Gnostic belief systems is adoptionism, and can be observed in Irenaeus' discussion of the Christology of Cerinthus:

He represented Jesus as having not been born of a virgin, but as being the son of Joseph and Mary according to the ordinary course of human generation, while he nevertheless was more righteous, prudent, and wise than other men. Moreover, after his baptism, Christ descended upon him in the form of a dove from the Supreme Ruler, and that then he proclaimed the unknown Father, and performed miracles. But at last Christ departed from Jesus, and that then Jesus suffered and rose again, while Christ remained impassible, inasmuch as he was a spiritual being.

Irenaeus, Against Heresies 1.26

Some people, like Vexen Crabtree, would suggest that all first century Christians were adoptionist. I would be hesitant to agree, as this is just too simplistic a representation of the diversity we find in early Christian thought. However, I would certainly agree that this is a view that is found outside of Gnostic thought.

So, we have two Gnostic Christologies here, one which was strongly disagreed with by Proto-Orthodox Christians, and one which was relatively common outside of gnosticism too.

This tells us that Gnosticism was itself diverse in Christological views, and we have two very different ideas of how Christ was divine here, so in that way i'd say it's difficult to argue that Gnostic belief systems as a whole influenced proto-orthodox Christianity.

Perhaps a better way to look at it is to view Gnostic belief systems and proto-Orthodox Christianity as organically growing from a similar background of Jewish thought and a hellenistic cosmology, which accounts for both the similarities and differences between belief systems. Christ's divinity, though differing in kinds of divinity, and in how that divinity was expressed, is part of most of these belief systems not because one influenced the other, but they all have very similar origins (aside: the philosophical and cosmological significance of the word logos is a good place to start).