Yes, if you had a perfectly ideal voltage source capable of maintaining a constant non-zero voltage differential between its terminals, regardless of what's connected between them, then you could theoretically obtain an unlimited amount of power from it just by connecting more and more loads in parallel.
For example, let's say that your voltage source provides a constant voltage differential of 1 V, and you connect a 1 Ω resistor across it. Now, per Ohm's law, a current of 1 V / 1 Ω = 1 A will flow through the resistor, generating 1 V × 1 A = 1 W of heat in the process.
But if you now connect two 1 Ω resistors in parallel across the same ideal voltage source, then a 1 A current will now flow through each of them, generating 2 W of heat. And if you connected $n$ such resistors in parallel, then a 1 A current would flow through each of them, and you would get $n$ watts of heat output in total, for any number $n$.
Of course, in practice that won't happen, because there's no such thing as a perfectly ideal voltage source.
In fact, the thought experiment above shows exactly why such a perfect voltage source cannot exist: by connecting arbitrarily many parallel loads to such a source, we could obtain unlimited power from it.
What happens in reality, if you try to do that, is one of two things:
First, every real voltage source has (or behaves as if it has) some non-zero internal resistance, which causes its output voltage to drop as the current draw increases, limiting the maximum power the source can deliver to less than some finite number of watts. If you're lucky, the source can safely supply this much power, and nothing else happens.
If you're not so lucky, the source is not designed to be safely short-circuited like that, and will overheat or otherwise fail. If you're really unlucky, it might overheat so fast that it explodes or catches fire.
That second possibility, by the way, is why all the electrical wiring in your house goes through a fuse or a circuit breaker. The national power grid that your house wiring is connected to is just about the closest thing to an ideal (AC) voltage source you can find, and could, in theory, supply a huge amount of electrical power without any noticeable voltage drop — way more than the wiring inside your walls could handle without overheating and catching fire! Those safety devices are specifically designed to fail (reversibly, in the case of circuit breakers) and break the circuit if you try to draw too much power through them (e.g. due to an accidental short circuit), and to do so first before anything else overheats and fails in a more destructive manner.