Here's how I interpret your question: if you don't take the promotion to full-line rep, how will other companies view you and your experience?
If that's indeed your question, my recommendation is:
1) think about where you want to live. if you don't want to relocate, you'll be somewhat valuable to other companies since you'll know the surgeons, OR directors, other key players, and be familiar with the health system landscape and politics. however, you'll be competing against folks who also live in the area and know all the same people you know, but they will likely be full line reps with more experience and more documented success. Start preparing mentally to think how you'll show that you had a direct impact on the territory and that you haven't gotten lucky as a one-hit-wonder.
2) if you don't care about where you live in the short term, take the promotion, relo, and stay with your current company at least 2 years. blow it out, keep all documentation of your success, and look for the right opportunity to present itself. proving that you were a successful ASR, then relocating to a totally different market and being successful there as a full rep speaks volumes to someone's ability to actually sell. I've known tons of people who look great on paper with documented success, but in reality they were only successful in certain environments. Great hiring managers will sniff this out. Being successful in multiple territories and ultimately covering different products (going from device to something different for example) is what separates the best from the others.
Good luck.