The Question boils down to, "What is immortality?"
If it is "Continued interaction with the physical world in a meaningful way," then no, she can, by her own admission, be cut off from that.
If, instead, it refers to a soul's being indestructible... Remember that Mr. Card is a man of practiced faith; he's mentioned this in interviews and author's notes. Mr. Card's flavor of religion does axiomatically believe in an immortal soul; it's safe to say that Mr. Card is at least open to that idea.
I find the presentation of Jane, and the Buggers and Pequeniños to be an examination of Soul versus Body...
- how many souls are in a Bugger colony?
At least one per queen. Possibly but not of necessity more.
- Is a Pequeniño's soul still in the tree?
Apparently, especially since the mind is definitely still in the tree
- Is Jane an ensouled Network? Or a soul embodied in a network?
Perhaps. This is, in fact, what I believe the central question to be pondered is for the existence of the character of Jane. We are to ask ourselves whether she's as human as a bugger colony, or a pequeniño. She's the third alien species of note in the Enderverse. If she is not a soul, then are any of the others? Are we?
Noting Card's theistic beliefs, Speaker and Xenocide both lead us to question the nature of Death. Jane is no exception.