Yes, you can put the neutral heroes into your team of 3 heroes in a 3v3 hero game. You can combine any three heroes you want, actually!
For each hero you choose for your Codex, you must put all of that hero’s cards into your codex, too. So if you choose Bashing/Blood/Fire, you will have all of the Bashing, Blood, and Fire cards, and none of the Anarchy cards in your Codex (and so you won’t be able to play any Anarchy cards).
If your three heroes are all the same color or neutral, your codex is “monocolor”. If at least one hero is a different color, then your codex is “multicolor” and you must pay 1 extra gold for the first tech building or add-on you build each game. So if your team is Anarchy/Blood/Growth, that has Red and Green heroes in it, so you must pay the penalty.
Any Red hero can cast any of the Red or Neutral starting deck spells (also called “minor spells”) normally. Same for Green heroes casting the Green and Neutral starter deck spells, etc. But if a Green hero wants to cast Red minor spells, it costs 1 gold extra. Same if a Neutral hero wants to cast a Red or Green minor spell.
Also, only a spec’s hero can cast that spec’s spells. So only Troq can cast Bashing spells, only Zane can cast Anarchy spells, etc. This is different from the minor spells just costing 1 extra, above.
That should cover it! Complete rules for 3v3 heroes are here, starting on page 10: https://www.dropbox.com/sh/oqxpfz2bpkln4hq/AADOTRd7FYucvULcbP3uKYpxa/codex_rulebook_46.pdf?dl=0