I doubt it. Cuneiform has neither the advantages of CHinese (it doesn't translate across language barriers)
Wasn't it adopted for Akkadian from entirely unrelated Sumerian?
In fact, I think I've heard somewhere that in most of the 2nd millenium BC, Babylonian-style cuneiform was the main script of most languages in the general area (Hittite, Elamite, etc - basically everyone but Egyptians and Minoans).
If you buy into the theory that Ponecian/ProtoSinai writing was inspired by the shapes of Egyptian heiroglyphs, then you could have them develop an alphabetic system inspired by cuneiform instead. That's not exactly "surviving cuneiform," but it would mean the survival of a tradition with cuneiform roots.
Wasn't this what Achaemenid-era Persian was?
IIRC, in the famous Behistun inscription, all three languages were written using some sort of cuneiform.
It's only those pesky Greeks that got in the way - if Persia won the Greek-Persian wars (and/or wasn't conquered by Alexander), their script might well have survived for a much longer time...
PS: Ugarit also did the same, about a millenium earlier. Persia was much larger, though.
PPS: BTW, if I understand it correctly, it's "Phoenician".