Don't know what you mean by aligning the grain horizontally with the string. The grain should be oriented perpendicular to the side of the bow, i.e., the rift or Vs should be on the top and bottom of the arrow as it is on the string.
Regardless, if you installed plastic nocks, they are shootable that way. A lot of arrow suppliers don't pay any attention to the grain when they install the nocks. They should, but they don't.
As already mentioned, the spine won't be as consistent; it will vary from 2-4# on cedar shafts depending on the orientation. Don't know what it would be on hickories. Could be more or less.
I wouldn't worry about breackage with hickories if the grain is fairly straight. They're tough as nails.
Of course, you can cut off the nocks and glue on new ones. If you made self-nocks, then wrapping with thread below them is a good idea, as has already been noted. Good luck.