Stealth during an attack: no, and it wouldn’t help much anyway
During the attack, you cannot use Stealth. That is, for the moment of the attack, your Stealth breaks, and you lose its benefit (which is that you were treated as having Concealment). Concealment is purely defensive and doesn’t improve your attack or damage in any way, so this barely matters.
Stealth while “springing”
You may, however, use Stealth during any form of movement – such as during a Spring Attack. That is, you could have a Stealth check to move up to the target, attack once, breaking Stealth, but then use Stealth to hide again as you move away. Hide in Plain Sight means you can do this, where ordinarily they would be observing you and preventing you from using Stealth.
You do have to move at half speed (or take the full-speed penalty) to do this.
This doesn’t help terribly much against your target (he is barred from making an Attack of Opportunity against you anyway), but might give you some protection against others who are in a position to take an Attack of Opportunity (they may not know where you are at all, and even if they do they take a 20% miss chance against you), plus of course it allows you to retreat to an unknown location which is useful for the rest of the round.
Which is great and all, but you’re getting one attack per round without any significant bonuses to it, and then retreating out of the fight so you’re not blocking anyone or threatening Attacks of Opportunity. That’s getting pretty close to sitting out the fight entirely at that point: your damage will be tiny and you’re not any kind of a presence on the battlefield.