Not really . Yes it will hurt but eventually he'll move on.

It would brake his Heart! 
 
Even so I believe in the pre-crisis. the original Kara was closer to Superman. 
 

With New Krypton blown to bits and all the Kryptonians dead and gone for real except for a scarce few, yosh, I'd definitely say that Superman would be DEVASTATED if Kara, his only living blood relative now, died.  I seriously hope that doesn't happen because I LOVE this newest incarnation of Supergirl and find her to be a more complicated character than Superman himself, she's a hero in the making, still learning and growing whereas Superman is already well established.

" @WW-Fan:    I think Powergirl is an older version of Supergirl from another dimension in the DC multiverse, so Supergirl is the Kara native to the main DC universe that Superman comes from. "

Then there will be supergirl V6, whatever

" isnt Power Girl the orignal kara? "

" @WW-Fan said:

" isnt Power Girl the orignal kara? "

No... PowerGirl is Kara from Earth 2 "

He'll get over it he's closer to Bruce and Diana than he ever will be to Kara

" @WW-Fan: Pre-Crisis there were Earth-1 and Earth-2. Supergirl was from Earth-1 and Power Girl was from Earth-2. "

" @Sha said:

" @WW-Fan said:

" isnt Power Girl the orignal kara? "

No... PowerGirl is Kara from Earth 2 "

the earth 2 Superman is the golden age Superman so Power girl must be the golden age Super girl ;) "

I'm sure Clark would be very sad if Kara dies, but he hasn't really shown much attachment to her.  After a grand show of caring when she arrived on Earth he let this 16 her old girl go live by herself with money sent to her by uncle Bruce.  A teenager, with little knowledge of the culture she's now living in, speaking the local language for only months, still hurting from losing everything she knows.  On her own, confused and (as we found out later) suffering from long-term low level Kryptonite poisoning (Krypto knew something was wrong, why couldn't Clark and Bruce figure it out?)  He had Ma and Pa Kent to take care of him, you'd think he would have shown a little more concern about making sure she had someone to talk to, to mentor her, to advise her and keep her out of trouble.  It made me want to call Interstellar Child Protective Services on him.

No wonder things worked out badly for her for so long.

After everyone died in New Krypton you would have thought he'd make sure she was OK instead of going off on a long walk in self pity.  After all, she lost family and friends, her mother died right in front of her eyes, the last of the heritage she grew up with was destroyed. He lost a bunch of people he didn't even know a year ago and a heritage that was as much his as being Irish is to a random person of Irish decent drinking a green beer on St. Patrick's day.

Right now I think his entire reaction would be how it affected him.  He's care, but he'd get over it quick.  Five years later it would be "Yeah, Kara... she was sweet, sure miss her.  Another beer Bruce?"

I thought Clark had lots of connections to his Kryptonian heritage... plus she's died loads of times in one way or another... he'll get over it... probably.