Your question is confusing for a couple of different reasons; it might well be similar to asking a Catholic if the idea of holy relics was a Catholic attempt to connect with people who believe in the Bible. Or asking a non-denominational Christian if their use of the cross was an attempt to connect to people who had faith.
First off, the City of Enoch isn't a doctrine of the Church that is often referred to, and isn't often challenged by those of other faiths. Most who believe in the book of Genesis (Christians, Jews, Arabs) all agree that God took him from the Earth prematurely (see Gen. 5:24
). The members of The Church of Jesus Christ of Latter-day Saints believe that Enoch had founded a city that was also taken up into heaven. -Here I am going to make a couple of assumptions, forgive me if I guess incorrectly. I presume you are not referring to a city that was taken from the earth years before Noah's flood. I would guess that you are drawing a connection to the Rapture and the Latter-day Saint's view that the City of Enoch shall return. The similarities exist (moreso in the minds of some than in doctrine), but I do not think they are all that alike. For those who do not know of the Rapture I will endeavor to elucidate: it is the name given to the time when Christ shall return to Earth, instigating the First Resurrection and then transporting all the righteous living up to Him and granting them the blessings of the Resurrection (much akin to the LDS doctrine of translation). The return of the City of Enoch is based off of a scripture in the book of Moses:
I shall prepare, an Holy City, that my people may gird up their loins, and be looking forth for the time of my coming; for there shall be my tabernacle, and it shall be called Zion, a New Jerusalem.
And the Lord said unto Enoch: Then shalt thou and all thy city meet them there, and we will receive them into our bosom... And there shall be mine abode, and it shall be Zion, which shall come forth out of all the creations which I have made; and for the space of a thousand years the earth shall rest. (Moses 7:62-64)
The timing (pre-millennial) is similar, and the supporters of one idea will often point to the same verses of scripture to 'give evidence' of their belief as the proponents of the other. Shy of that, the doctrines are not too terribly similar.
Another reason your question seems odd to members of the Church of Jesus Christ of Latter-day Saints is that you mention an attempt to connect with Christians. You will note in my (admittedly rough) attempts at parallel questions, just as most Catholics consider themselves to be believers of the Bible and most non-denominational Christians consider themselves to be people of faith, so too do most 'Mormons' consider themselves to be Christian. It is a little startling to be asked if a certain minor doctrine is an attempt to connect to a group that you are already intrinsically a part of.
Anyway, that is a long-winded explanation as to why we (and perhaps anyone else you may have asked this question) may have reacted by being somewhat shocked by it. On to the rest of your question.
The City of Enoch is important to Latter-day Saints for a couple of reasons. As was mentioned before, its return is associated with the Second Coming of Christ, an event to be eagerly anticipated and dutifully prepared for. Historically it was a city of powerful import, as it was so righteous in a time of such wickedness. As Sodom and Gomorrah stood as the bastions of all that is evil in the world, so did the City of Enoch stand as a citadel of purity. (The city was named Zion which is the Hebrew word for "citadel" or "fortress" [צִיּוֹן, tzyon
And the Lord called his people Zion, because they were of one heart and one mind, and dwelt in righteousness; and there was no poor among them. -Moses 7:18
This Zion, like the other Zions in the scriptures, was a gathering place of those attempting to flee the sins of the world, a place where like-minded people could all strive to live in the safety of the Lord. In one manner, members of the LDS faith believe they are living in Zion, as their faith in Christ provides a shelter from the storms of Satan. In another manner, they are striving to build Zion, seeking to strengthen their communities and homes against the struggles yet to come. In yet another manner, the Saints are looking forward to the arrival of Zion, the peace and safety that will come only when Christ Himself returns and brings the world His rest.Is not the way of heaven like the stretching of a bow?
The high it presses down,
The low it lifts up;
The excessive it takes from,
The deficient it gives to.(LXXVII,1-5)