You can usually take care of flukes with GC. Uronema and Brook would take up to 10 days of metronidazole. Then obviously as you mentioned copper for ich and velvet.
I'd say to answer your question yes, depending on what type of fish you are talking about it could easily carry flukes, Brook, or Uronema without symptoms.
Most fish are unaffected by Uronema and Brook. Any fish can carry them but not be symptomatic. For instance if it's a clownfish and Brook was present likely you'd know since it mostly affects clowns. However a Wrasse could carry it forever and never show a symptom.
Same with Uronema. Chromis, anthias etc. Would likely be symptomatic, but a tang would probably be unaffected.