All you lose without the coupling prongs is the metering on the less-capable F2 variants. The camera itself will still work fine - you'll just have to use an external meter (or guestimate, if that's your thing).
All metered F2 variants will meter with all F-mount Nikkors except those that require mirror lockup. Of course, the G series AF lenses only work at minimum aperture, but all metered F2 variants will meter at that minimum aperture.
The F2 Photomic, F2 Photomic S, and F2 Photomic Sb (single digit DP-n finders) require the shoe (AKA: prong, rabbit ears, annoying sharp thing that snags your pocket, ...) to meter at full aperture. Without the shoe, metering is accomplished by pressing and holding the DOF preview button while metering. The coupling pin on the finder needs to be tripped prior to mounting the lens for metering to be accurate in the stop down mode. The VF darkens making it "less nice", but that's how most TTL metering cameras worked in the '60s. This stop down metering method is the same on the F Photomic FTn and similar on all of the pre-AI metered Nikkormats. Methods differ slightly with the earlier F-series TTL Photomic finders.
The F2 Photomic A (F2A, DP-11 finder) and F2 Photomic AS (F2AS, DP-12 finder) require AI, AI-s, AI-converted, or any non-G AF variant to meter at full aperture. Otherwise, metering is done using the stop down method using the DOF preview button.
Said simply, the single digit DP finders meter at full aperture with any lens with a shoe and use stop down metering otherwise. Two digit DP finders meter at full aperture with lenses that have the AI meter coupling ridge, regardless of the presence or absence of the shoe, and use stop down metering otherwise.
BTW, the F2 body will mount all F-mount lenses of any vintage, though some require the removal of any Photomic finder for full utility (e.g early PC lenses). It is also the last Nikon body that can mount and use the 21mm f/4, which required mirror lockup and a special lug inside the lens mount.