Amperage rating of thermal fuse
Does this mean that in addition to its thermal fuse capabilities
  (blowing at a certain temperature profile), it also behaves as a 10A
  fuse,


No. 

Both current and voltage rating are the "safe operating conditions" for the part and your application should stay below these limits. Above this limits, the behavior is "undefined". Chances are, that the fuse will just pop at some point, but that's not guaranteed and you shouldn't design that way. If you need over-current protection, put in an extra current-triggered fuse.