Does adding the suffix -ly to a noun or an adjective provide morphological evidence for word class?

It does not provide evidence but it certainly narrows thing down. -ly attaches to nouns and adjectives. It tends to turn nouns into adjectives coward > cowardly, gentleman > gentlemanly and adjectives into adverbs quick > quickly.

But there are exceptions such as like > likely - here it is hard to determine whether like is a verb, noun or adjective but 'likely' is itself an adjective. Of course, due to the flexibility of English in its use of different word classes in other contexts, adjectives are often used as nouns. For instance, 'daily' which is often used as a noun when referring to newspapers or 'elderly' in 'take care of the elderly' or 'friendly' as in 'they played a friendly at Wimbledom'.

Of course, there are also many words that end in '-ly' where it does not indicate a suffix 'family', 'monopoly', 'Italy', 'monopoly'. Or it's not clear on the surface if it's a suffix, such as 'assembly' or it's definitely not a suffix but it looks like one as in 'folly'.

The best way to find out more is to go to a corpus and search for -ly on words with different parts of speech. Try BNC with search terms such as *ly.[n*], *ly.[j*], *ly.[r*].