If the definition is complete, then, yes.
This is an interesting question. In your example, someone who could bench press 225 for 12 reps would very likely have a higher 1 RM than someone who could only bench press 8. Things do get a little fuzzier when you get into higher rep ranges, however. For example, does the person that can bench 225 for 14 have a higher 1 RM bench than someone that does it for 12? Maybe. That probably could not be answered without conducting the experiment.
Further, the idea that strength can only be defined as the generation of force against an external resistance is one that is open to challenge. When we discuss this at the seminars, the example we give is the force the spinal erectors generate between each of the vertebrae. When you hold your back in extension on a deadlift, that requires force production at those sites and therefore strength. There is no good way to measure the magnitude of that force production so the "external resistance" portion enters into the definition for the purposes of making it much easier to quantify these things. Also, as CJ Gotcher and I have discussed before, when you do a pullup, where is the resistance? Is it external? If so, external to what? If not external, does it require strength to do a pullup?
Bodyweight exercises make thinking about this complicated. They require strength to perform, but quantifying that strength and comparing that strength between individuals gets difficult quickly.