I agree with Chris- I’ve read about people pausing a print part way to embed items, and then continuing the print. Some slicers (processing program you use to go from 3D model to printable item) have the ability to do this.
Couple of thoughts though-
3D printing is slow. It’s great for prototypes, or items that need individual customization. Unless you use a provider with a farm of machines lead time can be high. (There’s a place around the lower mainland whose name is escaping me right now that has a farm.) I’m assuming you’re thinking of 100’s of items at a time, if you’re already getting things manufactured in Asia (and I assume by injection moulding or similar.)
Embedding by pausing is going to need manual intervention part-way through the print. You can print several items in the same print run all at the same time, pause once, fill them all, and continue. Or you can print one item at a time, pause, fill, continue, and start the next item in the print run. The first way is great in terms of labor, but in my limited experience I’ve had more failures doing it that way rather than completing an item at a time. Especially with a material like Nylon, which I believe tends to curl during printing.
Does the thing you want to embed ever need maintenance? Does it have to be sealed?
Another option would be to design a cap for a cavity. If it has to be sealed, glue it. It’s probably a little more labour, but I think the failure rate will be a lot lower. And if the item to insert is an odd shape, a “fitted plug” could be designed that was split in two halves. Put the thing in the plug, put the plug into a regular shaped hole, seal it all up.
There’s a 3D Printing/maker meet up that the Richmond Public Library is organizing/sponsoring this coming Thursday at the Minoru branch. There maybe some interested/helpful people there. It’s the first of a series of monthly sessions. (Full disclosure- I’m the speaker that night 
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If you want really amazing finishes, and if the item is UV proof, you could probably do some amazing things with a SLA (laser + resin) printer. They have both solid and flexible resins now. You can write to them for samples. I have some that I can bring along to the library on Thursday if you want to see them.
Good luck!
Julian
