Don't see why not. (Edit: Except for the DMG errata. Should have read past the first post before replying. Sigh.)Song of rest seems like a cute little bard class ability that buffs p your healing rate with hit dice a little bit. However we have been talking about a mono class party for fun and games mostly to see what would happen.
Now if you had a 5 person party made up of 100% bards at level 5 song of rest restores an extra 1d8 healing to HD based healing. With 5 bards though if you spent a hit dice to regain hit points would you gain an extra 5d8 hit points per hit dice?
As rules exploits go, it's pretty tame. It doesn't make the party any stronger in a given encounter, just boosts their staying power across multiple encounters. And since all of the PCs are full casters, their staying power depends as much on their spell slots as their hit points.