Probably not, but it's your game. Some issues that might pop up, is if the CL is tied to the spell slot, or the spell being cast. Bloodrager 6 for example casting a 1st level Skald spell from a 1st level Bloodrager slot, would you allow the CL to be 6 or the Skald's CL probably 2 or 3.
A more unintended consequence is that it suddenly gets a good amount more "rages" per day, and they don't cause fatigue, but costs a standard action to activate. Someone under the influence of inspired rage can choose to gain the morale bonuses from another rage class feature that the character has. So the character can start Skald song, and gain the +4str/con from bloodrager, just not rage powers.
