If it is not hot plug mounted automatically, you can try mounting it manually.
Do you mean: “should it work in both windows and SuSE, and allow copying of data between the two OS” ? If that is what you mean, then the answer is YES.
What desktop are you using? fvwm? xfce? gnome? kde3? kde4? Some desktops have problems with automounting.
Now reference a manual mount of the USB stick, to do that it would help if you obtain some more information. First, I hope/assume you did NOT have your USB stick installed when you installed openSUSE? If so, that might mess up your fstab. …
Anyway, how about plugging your USB stick in and then open a gnome-terminal or a kde-konsole or an xterm and type:cat /etc/fstab
df -Th
su -c ‘fdisk -l’ and post the output here. Based on that we should be able to tell if your usb stick is /dev/sdb1 or /dev/sdc1 or /dev/sdd1 (or something else) and we can then explain how to manually mount your usb stick.