This is correct, similar to the way a monk with Flurry of Blows and Two Weapon Fighting can make full monk Flurry attacks and THEN take an offhand attack with the weapon, which is not required to be a special monk weapon. Whether or not a weapon is a monk special weapon is ONLY important when determining whether or not it can be subbed in as part of an attack in a Flurry.
So, like, a high level monk with 6 attacks in a flurry could attack with kicks and headbutts while holding a greatsword, then make an extra attack with the greatsword as a 2ndary attack using TWF, but could not attack with the greatsword as any of the 6 flurry attacks.