No.
Use execute to bleed off rage.
If you use Execute outside of a CS and that prevents you to cast 4 Execute during the next CS, it's a dps loss.
To maximize your dps, you want all your CS to be Execute - Execute - Execute - Execute.
The fury cycle is based on the idea that you are gcd-limited during CS so you want to use your spell with the better DPE, while you are rage-limited outside of a CS windows so you want to use your spell with the better DPR.
Because 4 Executes would be too good, so you should lower your dps on purpose?