This paper explores the possibilities for such a mission. It’s not that far fetched technically. But realistically, I don’t think it would happen, even if the object looked more interesting than it currently does.
Wasn't there a practical design using atomic bombs to propel a spacecraft? Alien artifact would certainly justify the budget and risk. Though if a country determined it was alien, they'd probably not share it until their craft was well on the way.
"Practical" in the sense of yes, the physics work, for the ones we know of. And assuming there was reason to quiet the Green crowd from freaking out about us launching nuclear bombs into orbit.
https://arxiv.org/abs/1711.03155