In a word, no. In the passage you cite, Paul is condemning divisiveness and a party spirit within a local church, not denominationalism.
From our perspective today, you might say Paul's teaching in this regard is applicable to each and every denomination, since every local church within a given denomination (or even a local church which considers itself to be "non-denominational," which the church of my childhood did) can manifest the same problem which Paul addresses in the passage in question.
Christians, as with non-Christ followers, are subject to the quite natural phenomenon of "having favorites." By that I mean we are naturally drawn more to some people than to others, especially people in positions of leadership. I suggest there is nothing particularly wrong with this. It can become unhealthy, however, when one leader and his or her followers set themselves apart from a local fellowship or denomination as a matter of pride. That is the issue Paul addresses in 1 Corinthians, chapter 1.
The church at Corinth (whether it consisted of one or more local churches) was afflicted by what I've called a "party spirit"; consequently, the seeds of divisiveness and discord were threatening to destroy the spirit of unity which Paul earnestly desired to characterize the Corinthian church, a theme he takes up again in chapter 12 in the context of differing spiritual gifts.
Again, there is nothing inherently wrong with being attracted to a particular minister of God's word. Where that attraction leads to a kind of loyalty which creates a spirit of separatism and superiority, however, steps must be taken to address and exorcise (so to speak) that spirit.
In Paul's day, some of the Corinthians thought that Apollos was the man for them and that somehow Paul and Peter did not quite measure up to Apollos. Others were siding with Paul or Peter, and still others, thinking perhaps they were the only "truly spiritual" ones in the Corinthian church, sided with Christ alone!
Now this party spirit can afflict entire denominations, but that does not mean denominations per se are unbiblical, nor does that mean Paul is condemning denominations in this passage. The spirit of favoritism which breeds a divisive party spirit, which in turn creates disunity within a church body of any size, including the church universal(!), must be eradicated.
Perhaps the only time when a "party spirit" can be helpful is when a serious doctrinal error begins to take hold in a church body, regardless of how limited in scope or how far reaching it may be. There are times, for example, when a contemporary "hot" issue becomes divisive and creates schism, particularly when a key doctrine or teaching of Scripture is at stake.
If, for example, a schism developed over the doctrine of Christ (i.e., Christology), with one group espousing the doctrine that Christ was not fully God, with the spokesperson for that group urging the larger body (whether a single local church, a group of local churches, or an entire denomination) to follow him or her in this (erroneous) belief, then church leaders (e.g., elders, bishops, district superintendents, ad infinitum) would need to administer spiritual discipline and root out the false doctrine, even to the point of the excommunication of church members.
We in the West live in perilous times, with hot-button issues threatening the unity of the body of Christ, locally and nationally. Gay marriage, gay leadership, denominational superiority (an attitude which says in effect, "Our group has a corner on the truth and those other groups which disagree with us are simply wrong"), abortion, the nature of the inspiration of Scripture (e.g., errancy versus inerrancy), and a host of other issues can be legitimate, biblical issues over which divisiveness is the unfortunate but inevitable result.
In such situations, what is needed above all else is a spirit of love which looks for biblical common ground on which conflicting factions can agree. Failing that, excommunication or perhaps other forms of discipline must be administered, but always in a spirit of love, with a view to restoration of the erring parties once they evidence genuine repentance.
In conclusion, denominations are not unbiblical, per se. In fact, if 10,000 more denominations were to come into existence worldwide, and each one held tenaciously to the central doctrines of the Christian faith (the Deity of Christ, the centrality and authority of Scripture for all things pertaining to life and godliness, the efficaciousness of Christ's death, burial, and resurrection for the forgiveness of sin, and several other key and necessary doctrines), I would rejoice.
As a Christian friend of mine told me once, we Christians cannot exhaust the ways and means of worshiping our great God and Savior, not matter how hard we try. Moreover, God delights in the variety of ways in which the unity of the church universal is demonstrated through the sheer sui generis nature of expressions of praise, worship, and love, regardless of how they may be expressed. As a wise person once said,
"In essentials, unity. In non-essentials, liberty. In all things, charity."
When this perspective characterizes a church body of any size or denomination, I believe God is honored and the body of Christ will flourish.