If there was solid evidence that it was of alien manufacture, we would go get it. No question. Access to something like that triggers 'national security' type responses. Projects under that heading have bottomless budgets and high risk tolerances.
Stuff like NERVA or Project Orion stayed proposals not because they're impossible, but because there's nowhere we really need to get that fast to justify the risks/expense/fallout.
"We need to get to this interstellar starship" would change the cost/benefit ratio of developing the tech needed.
Don't underestimate the gap between a science/jobs program like NASA vs what happens where there is an acute national interest. A derelict alien spacecraft would present an objective that no world power could ignore. Nation states taking enormous risks and spending hundreds of billions would make our current space program look like hobbyist work. In that setting, I would hesitate to say what is impossible.
In summary, you're pretty much right. If we could launch in 2017, we could have done it, but I don't think we have any spares of Rosetta or similar intercept missions sitting around.
Now - whenever people accuse me of never finishing anything I shall respond that I'm actually achieving TRL2 across a broad front.
Which is to say - I'm all for it! The sooner we make those breakthroughs, the better.