Have the Tyranids and Necrons ever engaged in a large scale battle?

No. According to source materials, the Necrons were asleep after their last great wars and stayed asleep until the 41st Millennium when they were awakened by Humans.

• The last great threat to the Necron before going into stasis was the Eldar who were at the peak of their power. The Necron knew they could not continue to fight having spent so much of their resources against the C'tan.

• So it was that the Silent King ordered the remaining Necron cities to be transformed into great tomb complexes threaded with stasis-crypts. Let the Eldar shape the galaxy for a time -- they were but ephemeral, whilst the Necrons were undying and eternal.

  • The Silent King's final command to his people was that they must sleep for the equivalent of 60 million standard years but awake ready to rebuild all that they had lost, to restore the Necron dynasties to their former glory. This was the Silent King's final order, and as the last Tomb World sealed its subterranean vaults, Szarekh destroyed the command protocols by which he had controlled his people for so long, for he had failed them utterly.

  • Meanwhile, aeons passed and the Necrons slept on, their machine slaves and constructs guarding them while they slept on Tomb Worlds that had been purged of all life to keep the Enslavers from their door. This plan worked with an amazing degree of success until the Necrons were awakened by the forces of the Imperium of Man in the late 41st Millennium to plague the galaxy once more.

• The Tyrannid had been encountered by Humanity and the Eldar as far back as the 35th Millennium but this would have meant, there had been no significant encounters before the modern millennium between these two powers.

No, the bugs usually avoid necrons. At least according to third/fourth ed lore.

The control of the 'nids by the "shadow in the warp" and the tendency of the necrons to close down the link of psykers to the warp don't mix to well.

I think one of the old codices (either 3rd or 4th edition) shows the splintered entrance of swarm kraken into the galactic disk and conjectures (point of view of an inquisitorial agent) that there is some kind of deterent square in the middle of what would have been the entrance corridor of a unified swarm.

A cut-away panel shows a lifeless planet/dead sun as the source of this deterrent. It is hinted this might be the tomb world of one of the remaining C'tan.

In Chapter 2 of the novel Dante, the Tyranids of Hive Fleet Leviathan were attacking the world Asphodex and other worlds in the Cryptus sun system. The Necrons awakened and used some weapon which caused a blast in space, and created a new star, which incinerated all the Tyranids in the system plus all the men on the system's worlds.