If I impregnate one twin will her identical twin sister become pregnant too?

In physics this is exactly what happens with quantum entanglement with small particles like photons ,neutrinos & some types of molecules etc..

Pretty sure it doesnt work with large complex organisms like twin sisters.

But if both sisters should somehow mysteriously come up PG you might try the quantum entanglement story & see if the family buys it.

Need not be necessary.

Now that would be a miracle!  There's one way to find out!  Assuming you're not doing both of them already.

No the sister won't (can't)! 

You are too stupid to breed.