Sounds and homophones

a) Let's take a kanji reading that is used only in compounds, and not as a word by itself, such as し for 歯 (if this is a bad example then please substitute a good one!). To native speakers, does the sound し by itself actually seem to mean "tooth" (as well as a whole bunch of other things, presumably), or does it only seem to mean "tooth" when part of a valid compound?

b) In English, homophones don't always come immediately to mind without context. For example, if someone said the sound /taɪm/ to me then I would think of "time" but probably not "thyme" straight away unless prodded or prompted. I suppose it is the same kind of thing in Japanese but more so, is it? Like with the sounds し, or かん, or whatever, do some common meanings come to mind straight away, and then the less common ones get increasingly harder to quickly bring to mind without context?

There's a reason on-readings tend to be described as (wordのkanji). し is not a word that means "tooth".

A better comparison in English might be "tele-". I think many native English speakers would first think of "television/things about television" (telethon etc) if they heard it alone (or mistake it for "telly"), and not the original greek meaning (although this would probably come out with prompting - "what does 'tele' in 'telephone' mean"). Since we never say "tele" alone to mean "far/over a distance", the mental connection isn't there.

Other than kanji which can have that reading standing alone, prefixes or suffixes might also come to mind - particularly if they're productive (can be used to make new words). Or very common ones (こく = 国). Not to overstate the obvious, but if that reading is not common for a given kanji, if the words that use that reading are obscure, if the kanji is rare, etc, it's less likely to come to mind without specific prompting.

If you asked for "all kanji you can think of that are read し",歯 would probably come up, although not as the first option, or if someone was to hear an unfamiliar word containing し and the context was right, 歯 might come to mind as a possibility. You might have had the last happen to you before - when you hear an unfamiliar word and your mind comes up with possible kanji for it. Not always the right ones, of course (at least in my experience).

Short answer? No. Japanese have far too few sounds to identify Kanji by their ON reading and you can't compare this to English where homonyms hardly ever exists compared to Chinese.

For comparison, Japanese have roughly 100 sounds with no tones. Chinese mandarin has 405 with 4 tones giving 1620 combinations.

When you use ON reading for a single character, these would be restricted to characters that are usually used by it self. If you say し, the first character that would come to mind would be 死 as this can be used by itself.

Also many characters in its ON form and it's usage in modern Chinese MUST be used in a compound. Again 歯 is one of them. 歯科、歯齦 etc. It would be ungrammatical to use it by itself as it would not be a word or anything but when in a compound, the meaning is understood. This is even more true in Chinese where there is no Kun. This is to avoid homonyms confusion. This is also why Onyomi words tend to be compounds.