HeyCat's Saturn, ruler of 6th house. Cat's health is Moon, ruler of his own 6th. I would say no, because the aspect between Moon and Saturn is too wide and is separatign, so any disease is in the past.
Also, Moon is peregrine but being received by you by rulership, exaltation and face. It's aspecting you (Mercury) and the Ascendant itself. You're on top of its health.
More important than that, cat's health has strong accidental dignity. Little guy/girl is fine.
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♍ Sun | ♒ Moon | ♎ Mercury | ♌ Venus | ♈ Mars Rx | ♑ Rising
"The detached one with the big heart."