Well it certainly depends on how rigidly one looks at the gospel message. No doubt, Hinduism and the gospel emerged out of different backgrounds, but they might, perhaps, share some imporant points.
Merging into the Brahman (Atman) and recognizing yourself as the totality of Being.
Its important to keep in mind that when entering into Brahman your temporal self dissapears. One does not become God per se, but one has uncovered that which lurks within and behind your temporal self; Atman, the immanence of Brahman.
Likewise, it is often said that the Holy Spirit is the immance of God, and that our body is a "temple of the Holy Spirit". I think alot of Christians take the implications of this too lightly. Quite truthfully, our body houses the immanent Spirit of God!
The entire gospel is filled with such little mytical hints. Not being in the first century and only having a small number of instructonary epistles, we can't know how these factored into the early Chirsitan's spiritual practice.
For example, Jesus said "love your neighbour as your self"....but yet, if everyone followed this and truly loved one another as their own being....what of the self would be left? We would dissovle into one another...
Or Jesus' famous quote "He who wants to save his life will lose it....but he who loses it for my sake will save it". Meditating upon this small puzzle yields some fascinating insights! In order to gain our life it must be lost... (a mystic would see this has profound meanings on multiple levels)
Its also intersting to note that Paul sometimes talks about Jesus, as though he was the embodiment of what Hindu's might call the Atman. In Colossians we see a picture of the Cosmic Christ:
"For in him all things in heaven and on earth were created"
"He himself is before all things, and in him all things hold together"
"For in him dwelt the fullness of God"
"He is the image of the invisible God"
Yet Paul reveals a great mystery that has "been hidden through the ages" but has "now been revealed to his saints", the glory of this mystery is "Christ in you".
Christ, in this epistle, is much more than a single being, but a cosmic and pervasive reality that
"holds all things together" is
"before everything" and
the thing in which "the heavens and the earth" were created. Importantly, the secret is that this living principle is within you.
Compare this to the Atman in the Upanishads, the Atman is "that which rests in the worlds, but is distinct from them, of which the worlds are the body"...."that which rests in all creatures, yet is distinct from them, of which the creatures are the body"
Paul is writing in a theistic tradition, its difficult to imagine, if one where to place some of these Hindu ideas in a theistic background, the portrait being much different.
Hinduism was always strongly philosophical, thus it espouses these ideas in elaborate philosophic systems. However, Judaism wasn't so. The mysticism of the Judeo-Christian tradition then are found hidden and scattered throughout the scriptures....the philosophy is not laid out but must be expunged from it.
And in the end...Christianity seems to be nothing unless one learns to see Christ within. This is the liberating force, the atonement message of which the gospels speak; death to the temporal self, rebirth in Christ. Who knows what metaphsyical affects this realization will inccur?