Another (typical) excellent delineation by Culpeper!
Using an alternative method (Ankara horary) I would have gotten a "probably yes" answer, but not as definite as Culpeper's (for me, cat = 6th = Moon; querents = 1st = Saturn; Moon flows toward Saturn-cat goes toward querents-, querents in cats home, ie 4th house from the 6th, with Saturn there in exaltation and the significator of the cats home being Venus, posited in querents house of Capricorn; and the cat-ie the Moon-is in querents home, ie the 4th house from the 1st, Moon posited in Venus in its exaltation, and the house lord, Venus, posited in querents house of Capricorn; so I would have given a "probably yes" answer, but not as definitely positive as Culpeper)
Congratulations on the cat's return!