Depends, the original release of 1.0 had bonus items included and these theoretically should still be redeemable (they were codes you have to redeem in your FFXIV account on the Mogstation). If you never used the codes you could try and should still be able to get the items (I presume by 'deluxe edition' you mean the Collector's Edition which included an item code for the Onion Helm). Additionally, the serial code for 1.0 is still redeemable as an ARR code if you haven't yet bought ARR (which basically upgrades 1.0 to ARR, but only the PC version).

Other bonuses required a 1.0 character active and transferred into ARR, and not just "I bought 1.0 but never signed up for it or used it", such as the Legacy Campaign bonuses like the Legacy Chocobo, or "only available in 1.0" goodies like the original Gobbuue mount.

So yeah, the only bonus I can see that you could get would be the Onion Helm, which should be still redeemable on the Mogstation if you have the voucher code from the 1.0 Collector's Edition for it still.