So history has been re-written in DoFP, which has basically ret-conned the first 3 films out of existence (although, they seem to have significant similarities, so perhaps they don't deviate too far).
As Wolverine is dredged from the river by Stryker, this would infer that in the new continuity Wolverine does undergo the adamantium procedure: that's what the scene is setting up, the very point of it.
Channing Tatum has just confirmed that he will be playing Gambit in a Spin off, and there are strong indications that Fox are trying to build a shared-universe like the MCU. The next X-men film, apocalypse, is said to be using the first-class era roster, with the new addition of Wolverine. Considering that Gambit has already appeared in X-Men Origins, he is supposed to be around 25-30 years old in the 80s, meaning he could appear alongside them. There is enough evidence here to assume the next film will be part of filling in the gaps between DoFP and present day...