Is it correct to say "I noticed how much passed since we connected." Would one deduce time by reading this? Or you have to specify "time" after much?
Yes, you have to use the word time. In the sentence
Much time passed.
the word much is acting as an adjective, telling us the quantity of time.
Now, much can also be used as a noun, with various meanings, all rather abstract. Usually, as in the sentence
the word much means "a great deal" or "a great quantity" in some generic sense. A good synonym would be "many things". But this usage of much has nothing to do with time.