What would happen to Deadpool if Adamantium were to be injected into him, as it was with Wolverine? The only reason Wolverine was still alive, despite Adamantium being poisonous, was because of his regenerating capabilities, and Deadpool has the same capabilities.
Most likely his bones would be replaced with Adamantium similar to Wolverine. If Deadpool had this operation done he would not however have claws like Wolverine as Wolverine's mutation included the claws in addition to his healing factor.
He probably could have handled an adamantium skeleton just fine, with similar effects as Wolverine's-- he would eventually age due to adamantium poisoning affecting his healing, but it'd be a very slow process.
However, it's unlikely he'd have agreed to the adamantium infusion in the first place. It would reduce his capacity to regenerate, he doesn't need it to do what he does best (he uses regular weapons, not his own body), and he exploits the normal fragility of his skeleton to both humorous and strategic effect-- in Deadpool (2016) he cuts off his own hand to escape being handcuffed, with the severed hand permanently giving his captor the middle finger. This wouldn't have been possible with an adamantium skeleton.