No, but we probably could with enough fuel. The bigger issue is space dust. Hitting it at relativistic speeds would be like flying into a cosmic shotgun for the entire journey.
"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."