Is the economic behaviour of a competitive market as a whole the same as a monopoly market? We know that the price-setting mechanics and individual firm's behaviour in a competitive market are different with those of monopoly powers'.

However, the demand curves of both competitive market(as a whole)and monopoly market slope down.

So here's the question: can we view the competitive market as a whole as some kind of monopoly power?

PS: What I'm talking about is purely theoretical. Hence pure theory is ok for my question.
Intuitively, I would say no. The main power that a monopoly has is that the firm can change prices at will, whereas a competitive firm has no power over price. 

The competitive market demand curve slopes downward simply because of the law of demand. The typical procedure is to take the price determined by the aggregated demand curve as given and set the individual firm's demand curve equal to that. This seems peculiar (to assume to know the market demand before you know the firm's demand), but given the assumptions of perfect competition  (particularly perfect knowledge), this does make some sense. If every firm has perfect knowledge of demand for their good, then they inherently know the market demand curve. The reason why this is important is because that is how you derive the price taking behavior of competitive firms.

Now that we have determined why price taking behavior exists, we can discuss whether competitive markets (as a whole) can behave like monopolies. The answer to this is that it would be nearly impossible for an aggregate competitive market to behave like a cartel (monopoly). The reason for this is because of the perfectly elastic nature of their demand. Suppose, somehow every firm agreed to increase their price to the exact same amount at the exact same time. Suppose further one firm had the ability to produce enough of the good to meet demand at a certain price. This firm (or any firms like it) would have a huge incentive to lower their price because by lowering their price (even by an infinitesimally small amount), they would instantly capture all of the demand for the good. If just one firm decides to cheat, then the whole market would end up right back at where they started at the original market price. For this reason, it is nearly impossible for an aggregated perfectly competitive market to act like a cartel.