The 60->72 pin adapters found in old Gyromite cartridges, as well as some other early first-gen games, looks like this when opened up (I can attest to this because I have one):http://www.vintagecomputing.com/wp-cont ... o7_big.jpghttp://www.classicplastic.net/dvgi/edit ... ert002.jpg
The cartridges that contain these are usually 7-screw (see first picture) -- 5 for holding the front/back casing together (these are your standard NES casing screws; older revisions usually can be opened with a flathead, but some may be reverse Torx), and 2 "internal" screws of a different size (larger, and silver) which actually screw into plastic posts in the casing. The "internal" screws actually hold the adapter in place -- without these, as well as without the large round plastic peg (which the centre screw goes through -- note the large circular hole in the Famicom PCB!),a Famicom PCB may wiggle/jostle around (this could impact reliability of the 72-pin connector making good contact with the NES itself, if there's a ton of mishandling).
Here's an example of a "non-official" 60-pin PCB (an Everdrive, actually! Note that the Everdrive PCB has a large circular hole in it -- now you know what it's for!) using one of said adapters in a Gyromite cartridge shell:http://i.imgur.com/msiz3VZ.jpg
This comes from this source (worth reading): https://krikzz.com/forum/index.php?topic=373.0
Could you use the 60->72 pin adapter in a NES cartridge shell/case that doesn't have the plastic posts for the adapter screws? Yes, but I would strongly recommend creating some kind of makeshift way for the adapter to be held in place very firmly. I'd think it'd be possible to create some makeshift plastic posts with holes in them (pre-drilled for the screws) which could be glued to the inside of a normal NES cartridge, at the correct spots. Another possibility would be to use globs of hot glue as makeshift posts (screws WILL go into them), but I'm not sure how well hot glue will "merge" or "connect" with the plastic on the inside of a NES cartridge. Maybe an alternate solution would be to make some kind of makeshift plastic filler that sits on the right/left sides and holds the adapter a bit more securely in place. There are several options, but most require work.
Sorry for the long-winded response, but this is more a manufacturing/moulding subject than "will it work". :-) Yes it'll work, but stable/secure case fitting may pose a problem.
Finally: thankfully the Namcot 340 doesn't offer the N163 expansion sound -- because if my memory serves me right, the 60->72 pin adapters *do not* pass audio through. (Note to readers: if I'm wrong on this, please correct me, I'm going off of memory when I did continuity tests some time ago)