So if it does detect them I'd imagine it would detect distal waves with high periodicity rates. The proximal waves are going to have very long wave length and I don't know how they'd disambiguate those without making very long observation windows.
Proximal sources of such waves are:
a) the Sun itself ...very very tiny micro shedding as it gives up mass to energy. These are likely to be super super weak and likely not capturable by current generation technology.
b) the Sun - Mercury transit , though Mercury is tiny compared to the sun both do distort space time and sit in mutual wells...which should create a very tiny wake (a GW) that has periodicity matched to the rotation rate of Mercury around the Sun. This being a longer wavelength it would require a long observation window and it is also abysmally tiny. So again ...unlikely to be captured with current tech.
c) the Sun - Venus transit …