If a non-creature permanent becomes a creature and gains counters that only apply to creatures, these counters will remain on this permanent even when it is no longer a creature. For example, if an Inkmoth Nexus is animated by its own ability and it gets a +1/+1 counter from something like Gavony Township‘s ability, those +1/+1 counters will remain on the Nexus. It does not matter that when the current turn ends the Nexus is no longer a creature. The counters will essentially not matter when the Nexus is not a creature. However, if it is animated later, the counters will affect the power and toughness of the Nexus.