A refugium with the intent of a refuge would be an ideal place for a seahorse for several reasons.
Water quality should be good, water flow should be ideal, food source (pods, etc) should be good, and there should be numerous places for the seahorse to latch on to with the Caulerpa, etc within the refugium.
Basically, a refuge is just that...a refuge, a place for lower stress out of the main stream of the tank. It is also utilized for additional filtration, etc by many people based on the above conditions. Adding a seahorse to this refuge would be an excellent idea. If the refuge is below the tank or maintained in a crappy manner...then the person desiring a seahorse to put in anything, shouldnt be concerned in obtaining a seahorse to begin with based on their failure to maintain the refuge in the first place.
Many refuges are near the tank, or a hybrid of a refugium is co-located with the main tank. These usually have excellent water quality as they are using the water from the main tank, lighting of their own, etc.