Was UNCLE headquarters ever invaded

Yes, THRUSH invaded U.N.C.L.E. HQ in the first scene of the premiere episode. Another time they attacked the headquarters of the European branch of U.N.C.L.E. by releasing deadly bees which killed all the staff.

The episode one attack on UNCLE headquarters was referenced in every following episode's intro with Solo behind the bulletproof glass being shot at, resulting only in the glass cracking from the Luger's bullet impacts and Solo's smug smile as he raises his own Walther. In some later episode THRUSH executives obliquely refer to this, mentioning their assault team who got inside were still listed as missing in action.

There is also a semi-comic season one episode with a British professor type mysteriously gaining access to HQ and raising havoc.

Checked and found it:

The Mad, Mad Tea Party Affair
The mysterious Hemingway causes havoc at UNCLE headquarters in New York through various means, including tampering with the facility's water supply and electrical system. This occurs on the eve of an important conference where UNCLE will host leaders from around the world. Meanwhile, Thrush's Dr. Egret and Riley, a Thrush mole inside UNCLE, conspire to assassinate the leaders. Solo and Kuryakin try to figure out Hemingway's motives. Virtually the entire episode takes place at UNCLE headquarters.

This show followed a pattern that some others also did, where the 2-part episodes were sometimes combined later as a "TV movie."

And the "real" movie was the reunion show, "The Fifteen Years Later Affair."