Again, this really depends on which Odin we are talking about, which Odin is being referred to as an Eikon, and the nature of Zantetsuken.
If Unukalhai is referring to the original Odin when he speaks of eikons, then this would seem to be correct. The mortal Odin required no followers to attain a truly amazing power (that we know of. It's possible he had followers of some kind, but we would never know). It would actually seem that the "true Odin" has more in common with the WoL/WoD than he does with a Primal, but that's a whole other thing.
If Unukalhai is referring to the Odin which we have fought, then it's not so simple. Similar to Shiva, "Odin" seems to only need a body and the sword. The sword simply acts as the crystal medium, little more than a great conduit of aether. Zantetsuken always remains after Odin's deathl, and it would seem that the sword has no worshipers ... only that's not exactly accurate.
No one has a shrine for Zantetsuken, certainly, but every warrior who uses a sword puts their faith into it. Odin (who was in desperate need for the strongest of weapons and pried this one out of an easterner's cold dead hands) put more faith into it than any other owner. He fought a whole war with it. Further, FFXIV already has a pretty well established basis for object worship with spirit bonding (which renders the weapon un-trade-able, and therefore unusable by any other person), aetheric weapon drops (which supposedly have the residual aether of the dead wielder trapped within) and the relic quest (Atma, Anmia, Zodiac mahatma / zeta). Zantetsuken has been around for more than 1000 years. Each new host feeds the sword their aether and possibly the aether of the enemies they defeat (if you follow the Anima/Zodiac lore). If you consider all of these things, then that's a lot of worship that has been provided to sustain its essence and an awful lot of followers who believed in the blade's strength.
Regardless, the nature of Odin (the current Odin that we fight) seems to boil down to the nature of his sword and how it has evolved over the time it has been killing people. It's entirely possible that it is simply cursed, and Odin's essence remains within the sword (probably via spirit bond) and is drawn out with each new host. This would imply that (assuming Zantetsuken is the "eikon") it requires no followers. However, it's also entirely possible that the sword itself is a primal that has been sustaining itself off of the worship of its hosts, tempering each new one as they prove their worth by defeating Odin's incarnation and living off of their aether. Given that the Dev's themselves have summed up the difference between the two words as little more than a language distinction (though they were still painfully vague on the topic) it's hard to say for sure which way this will go. Personally, I think it's a mix of the two, but only because I think it would have some pretty interesting lore implications for the Anima questline. We'll have to wait and see though.
Also, I too think that it is entirely likely that Odin's physical body is dead. However, the crystal imprisonment was empty when they examined it, and it would not be the first time that we've seen the Allagan's suspend someone's life for 1000's of years. That fact alone makes me hesitant to write off the possibility that he is still kicking. I highly doubt he is, but it wouldn't be the first time SE pulled the whole "suspended animation / sealed in crystal/aether/ blah blah blah" card on us.