I don't see why not.
No new class is actually 'based on Heroes of the Storm'. We're talking about using the Dragon Heroes as a 'visual aid' for what a Dragon themed class could look and play like in WoW, that's the context of there being a 'basis'. And as a general class concept, I don't think a Dragon themed class needs to be questioned at all.
I mean, if Monk wasn't already playable, I would say Chen and Lili Stormstout would be a great basis for a Monk class. And if DK's weren't playable, I'd say Arthas, Stitches, Kel'thuzad and Mal'ganis could all contribute in some way to formulate a playable WoW Death Knight class. It'd be similar to Illidan's look and gameplay ushering in WoW Demon Hunters. And I'd go as far to say Gazlowe is a good example of what a proper WoW Tinker could look and play like, as opposed to the more whimsical WC3 version.
We have multiple HOTS characters with a common Dragon theme, and a broad range of gameplay that isn't simply derivative of existing WoW specs. I'd say it's a good start as a basis, at least in terms of regarding a broad style of gameplay. We're mostly talking about broad roles (Tanking, Spellcasting DPS, Healing) and general ability themes, but I think it's something worth discussing.
As for what the class actually is, I think what Teriz presents has merit. It might not be my preferred choice to play as a Chromatic Dragon (I don't think they have a place in current lore), but the overall idea of a Dragon-based class that could actually be a Dragon makes sense to me. And the way he's presented the specs and the abilities is very easy to visualize, because they're not just 'words describing an ability'.
Some of them are already present in Heroes of the Storm. Takes some of the guesswork out of the equation.