No, it doesn't increase the value of the watch to have a third party convert a pocket watch like that but that doesn't mean the finished product has no value. Dont believe the old line that appraisals are an accurate representation of the true value of something. Many are done for 'insurance purposes' and are so inflated its ridiculous (jewelry & Art immediately come to mind) and others miss the mark on the low side. The only really accurate value is the one that someone is willing to pay for an item. There are a couple of Patek enthusiasts here on this forum but i would also suggest you post this same query over on the
NAWCC site where there are quite a few Patek enthusiasts. They probably wont give you a value but they're better suited to gauging interest in these types of watches. Best of luck!
Btw.... I'll suggest that you'll need to up your game in taking photos when seeking opinions on the NAWCC. 😉