Over on the site that must not be named, the general consensus is not really. If you test positive once, you’re immediately quarantined off the ship (River) or on the ship (Ocean). For River, you’re pretty much done with the cruise at that point. For Ocean, you continue to get tested onboard each day, but aside from that things seem to vary depending on the cruise. The minimum time in quarantine appears to be five days, no matter how you test after that initial positive.
This is all just anecdotal. But far as I know, Viking hasn’t stated specifics about their quarantine policies. So anecdotal is what we’ve got.