They certainly care about the heritage, as they milk it all the time to promote new watch sales - Speedmaster being the obvious example. But that's really as far as it goes. I think the fact that in their museum they have many watches that are not really correct illustrates that they really don't care much about the kind of things that collectors do, but collectors are a very small portion of their business. I saw an interview a while back where the head of Omega said they sell about 2,000 watches a day on average if I remember correctly. I suspect the majority of those are sold to people who are just looking for a good watch, and are not even enthusiasts let alone collectors.
As for 3D printing, being able to produce a specific shape is only a very small portion of the battle. Many parts inside a watch are assemblies that have different parts made of different materials, with very different engineering properties. Even something as simple as a replacement train wheel is quite complex. You have the shaft/pinion made of carbon steel that has been heat treated mated with a brass/glucydur gear. So even if you could print both parts that make up this assembly, you would still have to stake them together. Also, the surface finish of the pivots and teeth would have to be good enough for use in a watch - the pivots would likely require finishing to final size and burnishing at the very least to make it useful. Not sure how you would finish the gear teeth off well enough to make them functional.
A train wheel bridge is made of brass with jewels pressed in place, so this would mean printing the bridge and then possibly reaming holes to insert the jewels, making sure that all the depthing is correct between the wheels. Jewels of course can't be printed - they are grown and then machined to final size and surface finish requirements.
How about a reversing wheel:
Worn one on the right and new one on the left - can't see this being printed any time soon, not to mention a mainspring or balance spring...the list goes on and on. This one is from a 7750, but even the winding wheel in a Cal. 550 series is a complex little assembly:
A "balance complete" is made of a staff, balance wheel (with or without screws), balance spring collet, balance spring stud (glued or pinned), balance spring itself, roller table, and impulse pin (jewel usually). All these parts are made of different materials.
When people talk about printing parts, I'm not sure who they believe will be doing this, but it's not likely something your local watchmaker is going to have in his shop due to the complexity of the things I've mentioned here. If they won't be doing it, then it would require a company that has the resources to do this, and they would need to pick and choose parts that would be worthwhile to produce in some volume, as one off parts would be extremely expensive.
Not saying this won't be done in the future, but it's a long ways off in my opinion, and the economics of it have to make sense. Will there be any independent watchmakers left by the time this becomes technically feasible and cheap enough to be a viable solution rather than sending your watch to Omega? Not so sure about that.
Cheers, Al