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This experiment falls in the class including Mamra,
http://www.chessvariants.org/dpieces.dir/mamra/mamra.html, who moves like
non-royal King and cannot be taken by piece, only by Pawn. Okay, Immortal
returns to the capturee for later drop, and contrasted Mamra is gone for
good. However, using the description of Immortal as complete, compensating
additional difference is that the Mamra pawn-lost can in effect be replaced by
promotion, even twice or more. Mamra become
well-placed really ''gobbles up (almost) entire army one by one,'' and very possibly opponent might be doing the same at the same time, or if not, just attacking anyway with regular long-rangers whilst the one-side's Mamra
goes on the frenzy to no avail. ''Brute force playtesting'' is not
brutal but subtle.  Any new cv not computer-readied plays out that way.
Typically player preliminarily estimates value +/- 1.0 each new p-t compared to
known p-ts around or related, and by game two the estimate seems like +/- 0.5, each refresher becoming
more refined per games played. This Mamra-variant-Immortal slotted as an additional
piece on 64 squares versus regulars and backed by regulars is more than a
Rook and less than a Queen, first-approximate. Be willing to keep two
Bishops without Mamra-Immortal against opponent's Bishop-less M-I. Or it
might tip just over that and so the reverse, but no way high as Queen value. In other words, a good fair Betzan C.D.A. match-up could be RNIQK-NR v. RNBQKBNR, Immortal anticlericals versus F.F; better, let '-' be Barrier Pawn to make army of 16, RNIQKbNR, 'b' the barrier pawn and 'I' Immortal Man of endless-drop description.
In the same class is that weak-value Barrier Pawn(1948): http://www.chessvariants.org/large.dir/kristensens.html.