In British English, the distinction here would be between cucumber slices or whole cucumbers. 'The salad had cucumber' would usually mean a cucumber that had been sliced, and 'The salad has cucumbers' would mean that it contains whole (presumably smaller) cucumbers. It would be the same with 'tomato' and 'tomatoes'.
On a similar note, I never recall hearing 'cucumbers' used in this way in England, as we only really use large cucumbers, so they are always sliced.
The translation to American English should be cucmbers. To say "the salad has cucumber" would sound odd. Adding "a" before salad additionally wouldn't work as that would imply a whole, unsliced cucumber. The only way the translation makes sense in American English is with "cucumbers."
It is more to ng than to gg in this word. The absolute gg pronounciation is wrong, even we cannot say that this word comes from a Greek word with something γκ or γγ of Ancient Greek, but a Medieval one. https://el.wiktionary.org/wiki/%CE%B1%CE%B3%CE%B3%CE%BF%CF%8D%CF%81%CE%B9
I once ordered a salad without a boy! The man knew exactly what i meant and i also knew my pronunciation wasnt correct. When i repeated myself to include a more pronounced ng instead gg i was understood perfectly. I agree that the audio is much heavier on gg rather than ng...angori rather than aggori.