He would if given the opportunity and even when not. What he chooses to do is based on whim so there may be no way for Yu to properly avoid it.

"A minor curiosity." Still, he hasn't moved from the doorframe to let Yu in. Don't mind the moogle bobbling past Yu. She already has a few gold pieces of her own Gilgamesh has adorned her with as she slips past with a small bags. Saber is much more docile than her companion here at the door, and may pop back around just to scold Gilgamesh with those annoying 'kupos' to move.

"No one asked for you opinion." He comments lazily. Obviously she knows Yu is free to stay and Gilgamesh just isn't having it.