Currently, on every computer I'm aware of, if I copy an all-caps paragraph and paste into the middle of an all-lowercase paragraph, the pasted text will still be capitalized. Similarly, if I click into an all-caps paragraph and start typing without caps-lock on, the new text will be lowercase.
Italics should work the same way.
Note: I am aware that capitals, unlike italics, are different characters in Unicode/ASCII. Put that aside for a moment, it's not relevant to UI behavior, users don't care.