By purchasing the business, the current clients will give you a chance, but no guarantee that they keep ordering appraisals, as we are in a particularly fickle industry. The flip side is that other clients might not like the current owners as much, and prefer how you operate or appraise, but that is, of course, not what you are purchasing.
You would have the benefit of possessing prior files, and won't have to measure in those cases, but the files still lose relevance over time.
Not sure if you are on the residential side or commercial side, but I recall an appraiser that passed away and his estate attempted to sell the business. Even though he was quite successful, no one purchased the business. Not suggesting that RE appraisal businesses are entirely worthless, but just know what you are buying.