That's really doubtful. Self's delegation-based inheritance was expedient for quickly implementing an object model instead of having to build a class system, the influence never seems to have gone any deeper.
The one big influence on Javascript was Scheme, that was the original idea, when Netscape's execs asked for a more java-style language for marketing reasons, special-casing a single parent slot was an easy way to bolt an object system into the thing.
From what little I looked at it, delegation (through parent slots) is everywhere in Self, it's used for inheritance but also for mixins and scopes chaining and… It's not just an object model, it's a core semantic principle and tool.