Would a small hole in a Faraday cage drastically reduce its effectiveness at blocking interference?
It's fairly common to make Faraday cages out of mesh rather than sheet copper, so you can imagine that a single small round hole is not going to degrade the effectiveness enormously. But the holes in the mesh must be much smaller than the wavelength you're trying to screen.
In particular, it's the largest dimension of the hole, not its area, that matters. A 1-mm round hole will allow much less leakage than a seam 10 mm long but only 1 um wide.
Regarding the actual use case in question:
Having built musical instruments and experimented with this tape in the past, I can say it's a complete waste of time if you're using humbuckers, since those pickups are designed to cancel hum anyway, and almost a complete waste of time if you've got single-coil pickups, since most pickups nowadays come with shielded leads. If you do a good job grounding the pots, bridge, jack, etc., you'll be fine with no extra shielding. (How's your soldering?)
If you absolutely must shield the electronics cavity, use conductive paint, since you can paint it into every nook and cranny. With paint, there are no tape overlap regions that may or may not be in good electrical contact, and you don't have to worry about the tape adhesive losing its grip when you leave your instrument in a case in a hot car, causing the tape to fall off the cavity wall and short out your wiring (unbeknownst to you!).
If you're using vintage pickups with unshielded leads, you may consider just sleeving your leads between the pickup and the electronics cavity in a tube of conductive tape (just make this on your own from a sufficiently long piece of tape), and grounding that tape to the pot body to mimic shielded modern pickup leads.
The effectiveness of the shield (with and without holes) will depend on the frequencies you're concerned about, since the maximum size of holes in Faraday cage is supposed to be 1/10 of the wavelength or less. Reality check: a domestic microwave operates at 2.4 GHz (12.2 cm wavelength) and has a shielded window with holes of 5 mm or less.
If we're talking about audio frequencies, your biggest concern will be the skin depth of copper which is about 8mm at 60 Hz, so a copper tape (which is often 35μm) thick is essentially transparent to such waves.
At 1 MHz the skin depth will be about 60μm so several layers of copper tape may have an effect. A wavelength at that frequency is still around 300m, so small holes will not matter. Note that if you're in an environment where an object less than 1 meter in size picks up significant audio interference at 1 MHz, nearby objects about a quarter-wave length (75m) should noticeably resonate (as in, long metal cables would "sing" loud enough for you to hear).
At 100 MHz the copper foil is really effective (with skin depth of only 6μm). The wavelengh is around 3m, so holes of reasonable size will not be of your concern.
Only if you're expecting radiation in GHz range interfere with your guitar, holes in your shield can become problematic.