I wonder if Elaine Benes would hang outr with “Old” Christine?
Trying to see how your thread title relates to the rest of your post.
…
I’ve got nothin.
The title is noting that, probably, Julia Louis-Dreyfus has either never been asked, or been asked a billion times, the question in the OP.
I don’t know if she’s been asked but the resultant plot seems obvious. The episode will start out with them being enamored with each other for their similarities, possibly including lesbian fantasy dream sequence, but in the last third, they will discover that their own secret self loathing (and/or competitiveness with the few things they are egotistic about) results in them hating each other with a vengeance for their similarities, noticing things they hate about the other that they subconsciously dislike about themselves but don’t realize.
Or else, whatever happened between Friends and Mad About You.
I’m changing the thread title for greater clarity.
Old: she’s either never been asked, or been asked a billion times
New: Would two different characters played by the same actor get along?
That way people can add other examples if they think of them.
I’ve never seen Old Christine. As I recall, Elaine has no female friends and I don’t see her starting now.
It would start out fine, but:
Jerry, George, and/or Kramer would either come up with some insignificant thing about her that would force Elaine to end the friendship, or they would ask Chritime out and she would say no, causing Elaine to end the friendship or they would go out with Christine and it wouldn’t work out, cusing Elaine to end the friendship.
Alternatively, they would get along until Elaine dated Matthew or Richard and ended it, causing Christine to end the friendship.
Han Solo and Indiana Jones would probably get along; in fact I almost consider them the same person given two very different lives. Both travel to exotic locales, are used to taking care of themselves in dangerous situations and are a little world-weary. Solo’s taken more lumps than Jones though, so Solo is a bit more mercenary and Jones a bit more idealistic.
Richard Castle might find Malcolm Reynolds a bit too cynical for his tastes as a friend, and would help Beckett track down and destroy Caleb. Jayne Cobb, OTOH, would probably find Marcus Hamilton just his cup of Evil.
No Christine is too much like Elaine, so the characters would hate each other. Remember when Jerry found the girl that was like him and got engaged, then found her to annoy him?
There’s tons of examples
Quincy ME finds Oscar Madison dead.
Dick Loudan sees Bob Hartley about why everyone in his town, except him, is nuts
Sam Malone gets another hernia and gets treated by John Becker
Allie is catering a party for Dr Mary Albright and the Coneheads crash it to visit the other aliens (Triple for Jane Curtain)
And that is just a start 
I think Major Tony Nelson and J.R. Ewing would not get along at all.
And they would all laugh at Captain Hammer.
What did Captain Kirk do to deserve being arrested by T.J. Hooker, and defended by DENNY CRANE!