Did the Gnostics have apostolic succession?

Wikipedia says:

[apostolic succession] is understood as a sign and guarantee that the Church, both local and universal, is in diachronic continuity with the apostles; a necessary but insufficient guarantor thereof.

We need to understand that apostolic succession is not a guarantee that anyone with apostolic Succession teaches the truth authoritatively, but rather that apostolic Succession has been traditionally recognized as a necessary prerequisite for such teaching. Therefore, even if the gnostics had apostolic succession (which I will dispute in a moment), this is not a guarantee that the doctrine they teach will be true.

There is not much evidence to even believe that Theudas is real. The only evidence we have is that Clement records that the Gnostics prop him up as a member of Paul's inner circle, and a receiver of "special wisdom" from Paul. However there is no evidence for this claim, and we have no writings from or referencing Theudas to evidence this besides Clement's records. Quoting again from Wikipedia:

Theudas was allegedly the name of a Christian Gnostic thinker, who was a follower of Paul the Apostle. He went on to teach the Gnostic Valentinus. The only evidence of this connection is the testimony of Valentinius' followers and Clement of Alexandria.

It's also worth noting that Gnosticism is not a denomination, but a wide set of beliefs, many contradicting each other, that claim "special wisdom" from God. Therefore to say that Gnostics have apostolic succession is rather misleading.

The doctrine of Apostolic Succession developed specifically to combat the Gnostic proposition that the "truth which sets one free" is not the property of the Church and its bishops, but is experienced directly by the believer. So the answer to the OP is "No." The Gnostics did appeal to certain apostles such as Thomas, Mary Magdalene, Phillip, Theudas and others. But they had no doctrine of an unbroken chain of apostolic teaching authority passed on from Jesus to an apostle such as Peter and thence to the bishops through the laying on of hands. Here is a summary of the origin of the Orthodox idea of Apostolic Succession:

...The doctrine was first formulated by St. Irenaeus of Lyons in the second century, in response to certain Gnostics. These Gnostics claimed that Christ or the Apostles passed on some teachings secretly, or that there were some secret apostles, and that they (the Gnostics) were passing on these otherwise secret teachings. Irenaeus responded that the identity of the original Apostles was well known, as was the main content of their teaching and the identity of the Apostles' successors. Therefore, anyone teaching something contrary to what was known to be apostolic teaching was not, in any sense, a successor to the Apostles or to Christ.

While some Gnostic churches were organized hierarchically, they tended to emphasize mystical experience of the Truth. To quote the Catholic Encyclopedia:

Gnosticism possessed no central authority for either doctrine or discipline; considered as a whole it had no organization similar to the vast organization of the Catholic Church. It was but a large conglomeration of sects.

Peter Holds the Key

The figure of Peter is particularly important in Catholic and Orthodox ecclesiology. Jesus famously gives the keys of the kingdom to Peter and declares:

I tell you, you are Peter, and on this rock I will build my church, and the powers of death shall not prevail against it. (Matthew 16:18)

For traditional Christians, Peter is the rock of orthodoxy. Gnostic literature, on the other hand, often portrays Peter as not truly understanding Jesus' teaching. Instead, it depicts other disciples as receiving the secret teaching of Jesus in private. This is particularly evident in the Gospel of Thomas, as well as other Gnostic Gospels.

And [Jesus] took him and withdrew and told him three things. When Thomas returned to his companions, they asked him, "What did Jesus say to you?" Thomas said to them, "If I tell you one of the things which he told me, you will pick up stones and throw them at me; a fire will come out of the stones and burn you up." (GT v. 13)

What is special about the doctrine of apostolic succession in the orthodox sense is that it emphasized an unbroken tradition of teaching, centering on Peter and the original apostles, and through them to the duly ordained bishops. Gnostics sometimes appealed to apostolic authority, but they did not develop the idea that Jesus' teaching was passed on to through ordained bishops to succeeding generations.