We don't have any spacecraft that can go that fast, do we?
"Going slow to avoid severe H irradiation sets an upper speed limit of v ~ 0.5 c. This velocity only gives a time dilation factor of about 15%, which would not substantially assist galaxy-scale voyages. Diffuse interstellar H atoms are the ultimate cosmic space mines and represent a formidable obstacle to interstellar travel."
Also if I'm not mistaken, Voyager probes were not even intended to live so long or leave the system.
If there were a reason to send a probe to another star as soon as possible and no matter the cost, there would be a way, maybe not fast, maybe very expensive, maybe something weird, but it would be done.