You do not need the implant to access Eternum. William's lore dump, Orion's dreams and his experience at the costume party, and the Andromeda tapes made it clear that Eternum can be accessed through the standard methods of astral travel (i.e. via dreaming, consuming hallucinogenic substances). The only thing the implant does is allow normies to be able to access Eternum anytime they want and in a more reliable fashion where the experience cannot be interrupted except in extreme cases.
Also, someone on Cari's Discord speculated that the Exit Portal Orion saw back at the gas station was made by him (though personally I think it's simply mental imagery that indicated that Orion was about to astral travel to Eternum), which could be proof of his yet-to-be-revealed status as an Immortal. Recall that William revealed that the Founder - revealed to be an Immortal - created the Exit Portal system as means for implanted normies to be able to travel to servers. The idea is that maybe Orion also has the ability to create them, albeit on a lesser scale compared to the Founder.
Opening the letter prematurely will lead to Orion reading out the contents of the letter, which reads:
"Askion kataskion lix tetrax damnameneus aision."
Googling that leads you to the Ephesia Grammata, which is a Greek axiom that provides protection to the person who utters it at the right moment. Interestingly, it also happens to be associated with the Cult of Artemis, a goddess who in some mythological sources was the lover of Orion's mythological namesake.
Anyway, technically the letter could help. But IIRC Orion can't access his inventory in the real world so...that could be a stretch.