These days, the general workflow has really evolved to assembling artifacts into "packages" and then pushing to a package manager; basically Build > Package > Deploy I think the reason is that it's much easier to deploy known packages (then assemble them from artifacts). In this case, ProGet serves as the Package manager step.

At this point in time, it is unlikely. However, Atlassian does mention on their site that plugins could be created to integrate with third-party tools, and the JSON ProGet API could be used for this.