It strikes me that "couple" and "couple of" are simply adjectives that mean 'an undefined amount', either 'many' or 'few' depending upon the context.  Because they are simply adjectives, there is no question of agreeing with the verb; that would depend upon the plural noun that heads the noun phrase of which they are a part.

 

My experience is that some speakers use 'of' and some tend not to use it.  But deleting the 'of' simply strengthens the view of 'couple' as an adjective. 

 

When we talk about a literal couple (e.g. a couple of people), we tend to use 'couple' as a noun, and we don't typically specifiy a couple of what; we seem to let the context do that.

 

--I drank a couple of beers.

--Did you have any beer? Yeah, I had a couple.

 

--A couple walked along the beach= two people

 

--A couple of people walked along the beach=there were some people walking, maybe together, but probably not in a pair.

 

Just my thoughts--

Linda Di Desidero