Looks like Boon Companion has some weird cases anyway, so here's another one to add to the pile:
Can a Druid with Racial Hit Dice take Boon Companion to make their animal companion more effective than the companion of a Druid of that level would normally have (but closer in effectiveness to a druid of that CR would normally have)?
If a Ranger with Racial Hit Dice takes Boon Companion, does it only provide the normal +3 Levels the Ranger's companion is delayed by? Or do the racial HD allow it to provide the full +4?
This is mostly relevant for monster NPCs or unusual games, but it can be a significant deal - if a wood giant hunter, or a nymph druid, or a janni ranger, or a yamabushi tengu samurai has an animal companion according only to their class level, it could be on the weak side or even basically irrelevant, but boon companion could make the companion much more commensurate with its master's threat level.
Nope. The way Boon Companion is worded in depends on character level and druid levels. It is not written in such a way that boon companion will make up for racial HD.
The game isn't designed for players to have any racial HD, so if you were designing an NPC I wouldn't see it as a problem. I wouldn't however let a player do such a thing, but I also wouldn't let a player play anything with racial HD either...
As a GM you shouldn't feel beholden to the rules when making NPCs. As long as you feel the difficulty of the fight is appropriate and you increase the reward commiserate with the difficulty it should be fine.
RAW: No, because companion stuff is all in terms of class/character level and HD are not technically equivalent.
(There is one place where they are:
Hit Dice: The term "Hit Dice" is used synonymously with "character levels" for effects that affect a specific number of Hit Dice of creatures.
However there is nothing that extends the scope of that outside of spell effects.)
RAI: Yes, because character level and total HD are equivalent in practice.