I don't have a V20 but my HD600 works a heck of a lo better on my iPad than my Note3. HE400S has higher sensitivity and low impedance, so that puts it at the meat of the V20 chip's powerband, and get louder with the same amount of power, so as long as you don't have to crank it up past where it's clean, it should be good. That said, note that:
1. It's a good way to listen when the power's out and I'm unlucky enough to not have charged my portable amp (has not happened since I got the D-Zero, which doesn't drain the charge even if I don't use it, or only use it as a DAC).
2. I don't walk around the house listening on an open headphone and I'd still use my amp with the HD600 a banging wok, meat sizzling on cast iron, clanging plates or bowls in the sink, much less power tools, will just go through the wide open earcups. Even my IEMs can't completely block those. Not to mention debris and any other accidents - smoking oil, fat popping off the skillet, faucet water splashing off bowls, a cat startled by a stupid vacuum cleaner or drill jumping up to my shoulders - can mess up my listening by messing up the gear a lot more than having to wait until I can sit down next to the amp.
3. Even a 99dB/1mW Grado doesn't sound all that much like what people mean when they talk about Grados when driven by a smartphone or an iPod vs, say, a CMOY or a D-Zero.
So what would matter more past the specs is how high are your expectations. Keep them low, and they'll work fine.