No. It'll grind up in a short while. I am thinking of the fan hub with the tapered roller bearings in it.
I am thnking you want a slight preload on the bearings when cold.
You have a clearance problem, Perhaps the new bearing cones were longer than the old ones. Or the cups were not as long.
You may have to put a shim behind the front cone to tighten it up.
P.S.: How did you get the rear cone out of the housing?