It won't hurt at all, but be forewarned: once a set of synchronisers go out, the rest tend to follow. I am not trying to scare you, only warn you. You will probably be fine for six months, as long as you pamper it... but there is no guarantee. Save up the money and buy a rebuilt unit.
The AX5 is a good stock transmission FOR A DAILY DRIVER BEHIND THE FOUR CYLINDER. My AX5 lasted 150,000 miles before I changed BUT I DIDN'T NEED TO. If you go off road, it is too weak and doesn't last long. Jeep had some major problems with this transmission and went with a more stout one in later jeeps. Every one talks bad about them but in my experience, for a daily driver and not being rough with it, it is OK.
You may want to consider upgrading to an AX15 which is a much stronger tranny but you have to find the correct bell housing and change the input gear on your transfer case. Also you will probably have to change your rear driveshaft. There are a few write ups on this conversion for your jeep in this forum or Jeep Forum.com . It is your choice. "NOVAK JEEP CONVERSIONS" on the internet would have good information about this.
I can tell you that my four banger and AX5 lasted a while and I was happy with it. I don't think I was the "exception to the rule" but then I tend to take care of my vehicles more than most. If I am off road and see a log across the trail, I drive around, not over. What can I say... I don't have the money to "roll my jeep" so I avoid it to the best of my ability.