I see no reason why it couldn't be implemented in current Perl, as infix ~~ doesn't clash with any existing operator.
There isn't a technical reason why it couldn't be implemented. I think the main reason it won't get implemented is that the people really wanting it aren't going to write the patch, and the few that do write large patches for perl5 have other priorities.
Write a solid patch that does implement binary ~~, addressing all possible backwards compatability issues, and you'll have a decent chance of getting the operator in Perl.
And that's true for all Perl6 features people want find its way into Perl5. Wishing for it won't get it implemented. Voting for them won't get them implemented. Discussing here how useful the features would be won't get them implemented.
The basic rule for adding new features to perl5 has been for several years: write a patch that adds the feature. Discussing the idea on p5p first might not be a bad idea, (if only to avoid doing work for something that won't get accepted). But unless you write the patch, or find someone to write it, it's unlikely to be added.