Giants coach Jon Sharp said Hudson's actions will not prevent him making his first appearance for the club in Sunday's pre-season friendly against Wigan at the GalpharmStadium.
As for Fa'asavalu, who was chosen ahead of Andy Coley, Nick Fozzard and Andy Lynch, he could make his GB debut in the first of three Tests against New Zealand at Huddersfield's GalpharmStadium on Saturday (1815 BST).
After an unsettled couple of weeks, following confirmation of captain Brett Hodgson's impending move to Warrington amid rumours that coach Nathan Brown will quit at the end of the season, it did little to lift the gloom over the GalpharmStadium.
The build-up to the game has been partly overshadowed by the news that full-back Hodgson will be leaving the club at the end of the season for Warrington and speculation remains over the future of coach Nathan Brown, but his playing namesake hopes that the former St George Illawarra coach will remain at the GalpharmStadium.