
Daniel Turner Zen Archer |

If you're asking if a bloodrager could rage during a Skald's Raging Song and benefit from the Skald's powers in addition to their own, yes except for a couple things that will only become available once the Skald reaches level 20.
Master Skald (Su)
At 20th level, a skald's inspired rage no longer gives allies a penalty to AC, nor limits what skills or abilities they can use. Allies with rage class abilities may use features dependent on those abilities without restriction, such as a barbarian's rage powers and a bloodrager's blood casting and bloodline abilities. Finally, when making a full attack, affected allies may make an additional attack each round (as if using a haste effect).
So the barbarian could rage under the influence of the Skald's Raging Song, but the Bloodrager couldn't cast spells in the same circumstance until the Skald reaches level 20 first.

Pounce |

I feel like the answer should be yes as well, given the way rage class feature is defined by the Skald:
..If an ally has her own rage class ability (such as barbarian's rage, bloodrager's bloodrage, or skald's inspired rage)..
If the skald has the ability to rage from another source, he can use his skald rage powers during that rage as well.