Fish is fish. 50 lb of Koi and 50 lb of Goldfish have the same basic needs. A few small Koi would likely be fine without a pump if some other measures are taken. Depth of pond, amount of food, your climate, and most importantly how you view fish...pets, cherished family members, decoration, etc... I'm guessing this will be an Aquascape pond which normally is more for a landscape feature than an interest in fish. The fish are more decorative. Many Aquascape ponds are cleaned once a year and new fish are added as need then.
To the question...I deal with HOAs here in Phoenix a lot. First, if they actually only asked a question then that's easy...YES, pumps can be turned off. Always be positive, flexible when just chatting. Only if they put it in writing as a condition of permission do you have to get into trying to convince them. If needed you can offer that if anyone has a problem you'd of course be happy to turn off the pump at any time. They're trying to cover their butts...help them. Besides, you'd be giving up nothing. Even with permission an HOA can still come back later and say sound or smell breaks the rules. So you're offering give them power they already have. People like that.
I also point out that the pond will have Mosquitofish so the pond will be a "mosquito sink". They'll ask what that is and you can tell them that instead of mosquitoes laying eggs elsewhere nearby they will lay in your pond where the Mosquitofish will consume them. So fewer mosquitoes in the neighborhood. Then list some horrible mosquito spread diseases like West Nile. Whatever disease is a hot topic in your area or is being pushed on Fox News. That stuff scares the crap out of people. They'll probably all want a pond.
Bottom line it's an HOA. You agreed to all the terms. Don't get bummed out. Lots of people here go to war with their HOA and that never goes well.
