For example, a colour filter array with deeper reds, or one with warmer blues or one with a kodachrome look etc. This is of course with Color Accuracy not being a priority here.
In theory, yes - although in general you'd just shoot RAW and then mess around with stuff in post rather than trying to modify the camera.
On the other hand, the extreme here is modifying the camera to be receptive to infrared light which would very definitely fall into the "colour accuracy not being a priority" side of things.
Some but not quite. Part of the look of film is "grain". In modern digital terms this is usually called "noise" but noise is a similar but not entirely the same concept.
Noise comes from the electronic signal being lower than environmental electromagnetic fields - the main one that cannot be eliminated is cosmic microwave background radiation which induces electric current in things (including you camera's electronics) but there are other sources of noise such as your wifi router (actually stronger than cosmic microwave background), any nearby computer, spark plugs in running car engines etc.
When your camera tries to process such low signals (eg. a very dark image) there's always a probability that some electromagnetic waves from the sources mentioned above will induce electric current in your circuit that's stronger than the image signal. What you physically see is dots in the image or uneven/spotty brightness in the image. That's noise.
Grain is caused by silver or dye particles on the film. The particles are actually what makes the image. When exposed the particles harden so during development the unexposed (or less exposed) particles can be washed away to leave behind the image (which is made out of hardened particles). Because the particles are literally molecules (or clumps of molecules) instead of a regular array of sensors (like on a digital camera) the distribution of the particles are kind of random. And random means it's not 100% uniform. The non-uniformity causes the image to be "grainy". It's similar to noise but doesn't look the same. Higher speed film (higher ISO) are more grainy because they need to be designed to be more sensitive to light (thus need larger silver crystals).
You can emulate colour grading with filters but you can't fully emulate grain, not even with noise. The best way to emulate grain is via software filters in post processing.
Color films alter their color response, and thus their "look" mostly by altering the color of the dye couplers in each layer of the emulsion. These dye couplers don't do anything until the later stages when the film is developed. They're sitting there dormant during exposure because they aren't light sensitive. The sensitivity of the three layers of silver halides that are exposed when struck by light aren't really that different between different types of color film.
The "look" of color negative film can also be altered at the printing stage by selecting different printing papers or by using color filters between the light and the paper when the paper is exposed by the light shining through the negative.
So in a sense we already emulate film with the way we postprocess digital images. When we change the color temperature and WB we're doing pretty much the same thing as changing the color of the dye couplers in color film. When we use HSL/HSB/HSV tools to adjust one range of colors without affecting the others, we're doing the equivalent of dodging or burning one part of the image with a color filter applied at the enlarger for only that dodge or burn step in the printmaking process.
For example, a colour filter array with deeper reds, or one with warmer blues or one with a Kodachrome look etc.
Most CFAs don't have any reds (640nm) at all, all of the cute little RGB checkerboards posted on the internet notwithstanding. Typically the "red" filters of most Bayer masks are most transmissive somewhere between yellow and orange (590-600nm).
This is to emulate our retinal L-cones (L = long wavelength) that are most sensitive to Lime-Green (564nm), even though we've called then "red" cones for far longer than we've been able to determine exactly where their peak sensitivity lies independent of our M-cones (medium wavelength) and S-cones (short wavelength).
For further reading here at Photography SE, please the following questions and their answers:
Why don't mainstream sensors use CYM filters instead of RGB? (Hint: most mainstream digital cameras have CFAs that could be most accurately described as YGV: Yellow -Green - Violet rather than RGB. RGB is what our emissive output devices use.)