What I'm trying to do is have this embedded into a hollow table, then I can use it to feed into a couple outlets elsewhere in the table to power a few things, like a low power computer and a printer.
If I understand your question, the answer is no. Or, yes, you "can". But no, you should not use a hollow table as the electrical enclosure for a home-made power strip unless the table was actually designed to be an electrical enclosure.
Instead you should buy ready-made boxes that do what you want. If you want to have power outlets embedded in a table, there are a lot of ready-made modules to do that. Search for "recessed table outlets" "recessed conference outlets" and so on. Some of them pop up in cute ways. Some of them have built in USB charging. Most of them have built-in power cords under the table presumably because that is cheaper than using an IEC connector and avoids the risk of users kicking the cable out. But some do have female IEC connectors instead so you can use separate power cords. Some of them can be daisy chained so you can install recessed outlets in different parts of a large table, while having only one power cord connecting the table to the wall or floor. That sounds like what you want to do, but a lot safer.
If you use daisy-chained ones perhaps you could route the double-insulated cables between them through your hollow table. Again, a more ready-made way to do this would be to install a $2 plastic channel under the table, or just use staples.
All my links are the results from random searches, just for illustration. They may or may not be what you or anyone should use for your purpose.
The NEC doesn't regulate devices but wiring & wiring methods for structures. This is a case if all components are UL approved components are used and wiring methods yes you could create a “power strip” of sorts with multiple receptacles.
This would be much like building a home made lamp using listed components it is legal but you can not sell them in the US without being approved by a 3rd party vendor. If the components are not rated for 20 amps it would be smart to incorporate a overcurrent protection device to prevent a fire. Make sure all points are finger safe or you can not get shocked when it is plugged into the wall.
Complete power strips that take a 10A IEC input (on a cable extension or directly), have mounting flanges and optionally also come with IEC outputs are readily available - though they are not available much in super cheap, low quality versions, since their main use is in datacenter and industrial control 19" racks. Search for "PDU". Most of these incorporate a fuse or breaker to make sure that the input connection is not loaded above its rated ampacity.
Also, for 13A/16A circuits, there is a larger version of the well known IEC C13/C14 system, C19/C20.