no, not quite there yet.
What you want is relatively fast growing wide growth rings that are at least 1/16 thick. when rings are too tight, growth too slow, the wood tends to be brittle. Now if you were making a handle of yew, the opposite would be true;tight rings.
Looking at the center end grain ring you should be able to follow the line of the ring fully down both edges of the helve. (at the pole and bit the wood is called edge grain) Next follow the two on either side; they too should remain continuous- not exiting the side. continue following the rings end for end until you find the one(s) that do. Notice it makes an "arrow point >>>) on the face.(the surfaces with arrow points are face grain)
If the helve is completely true those arrows points will be centered on each face. But usually what you see is some slope to the edge grain, with bias that runs out on one side or the other. Shaping cuts through the ring-this makes the point so naturally not every ring will run continually end to end. Slope is different though = bad.
You can also have bad run out on the face but this I think, is more common when someone makes their own handle from sawn wood rather than something that happens often in commercial made axe handles which also happen to be sawn from the log.
The best helves are made from billets split from straight grained logs. The split naturally follows the growth rings. Which means the best are home/ hand made. Some may have a hard time accepting it but when split out there is not so much difference in a helves tendency to break One could orient the grain perpendicular to the bit..... but i've already tried to explain that once before