Short answer:
No
Explanation:
Here are some examples of where this question might arise:
I play Vilya on my Elrond, which is subsequently returned to my hand with Call of Home. If I play Elrond later in the same turn with A Chance Meeting, does it still have the bonus from Vilya?
My Hero opponent is moving to Cameth Brin, and I play Whole Villages Roused on the site, causing the site to gain the automatic attack indicated on the corresponding Minion version of the site. But my opponent played Master of Esgaroth at the end of their organization phase, so after the Movement/Hazard phase is over, they decide to move to Rivendell. We both draw cards, and after I play hazards on the company, my opponent plays Bridge (at the point that Cameth Brin has already been returned to their location deck). After drawing/discarding to eight cards, my opponent declares that their company is moving to Cameth Brin again. Is the effect of Whole Villages Roused still active?
The answer to these two questions (and similar ones) can be answered by referring to CRF, Rulings by Term:
This also means that the effects of other cards played on it (Vilya, Whole Villages Roused, etc.) also cease having an effect on play when the affected card leaves play.Discard
If a card leaves active play, including being returned to a player’s hand, it immediately ceases having an effect on play.