If you look at your glass and see white specs that hop around, you have copepods

. If the specs are big enough that you can see legs, then they are not copepods. Adult harpacticoid copepods (the kind you're likely to see on the glass) will be about the size of a pinhead or maybe two pinheads if they're really large.
How big is your tank? I think whether or not you need a separate refugium likely depends on the amount of live rock you have. Have you heard of the term carrying capacity? Its used in biology to mean how many of any particular species an ecosystem can support. Your tank is an ecosystem so ultimately whether or not you need a fuge or to add copepods regularly depends on whether or not your ecosystem can support (provide food and safe places to breed/grow up) enough copepods that they are not extirpated (removed) by your fish. My tank is 20 gallons and my fish (rough head blennies) are really only interested in eating live pods. I don't want to risk their lives/health and since my tank is so small I'm not confident that the amount of rock I can physically fit in it could provide enough places for copepods to breed without all being eaten by my blennies and I don't want to pay to add pods every month so I have a HOB refugium. If my tank was 120 gallons I might feel differently and see how it went without the fuge.
I think for small tanks (under 75 gallons) with fish that rely on pods for health/survival, its a good idea to play it safe and have a fuge. Not everybody will agree with me of course and I know that 75 gallons is an arbitrary number. If I was trying to keep two mandarins in a 75 I would probably want a fuge.
The point is more that you have to think about ecology, carrying capacity, and how much you're willing to risk the lives of your fish. I definitely *don't* see how you would have to add pods every month if you have a fuge, unless you had some event that wiped out your entire copepod population in the fuge as well as the DT.