Probably not.
Should I be spending money to market my free app? The answer is no. You should not be spending money to acquire users for your free app. It's going to make a bunch of numbers go up, and all of those numbers are going to go back down. You will find yourself right back at the starting point.
In almost every instance where a free app or a consumer app has gotten really big, it's because the founders have found some nonobvious way of cheaply getting their product in front of a large number of people. Even if your CPM is not that high, it's essentially a way of kicking that can down the road.
The one exception that I'll give for this rule, in my mind, is that if you're going to experiment with paid acquisition in some way, the thing to keep in mind is that you should limit the amount of budget that you spend. You should be very clear in what you're trying to learn ahead of time.
Be clear ahead of time that what you're doing is not buying users; it's running an experiment to learn something specific.