Yes, of course so long as it obeys the rules of quantum mechanics. That is, you can't say that "everything is possible, so the possibility that quantum mechanics is wrong might occur, so it is wrong". Those are not the kind of predictions quantum mechanics can make.
Let's look at the kind of predictions quantum mechanics can make. To do that, let's consider the quantum information stored in your brain. If all the important information in your brain counts on the positions of $10^{23}$ "particles", then the thing encoding all the knowable quantum information about your brain is a function of $3\times 2\times 10^{23}$ variables. That's a huge thing! It describes all the quantum weirdness of your head interacting and being entangled with the rest of the universe.
That thing is the "density matrix". A density matrix is like a quantum wavefunction, but I use it here because your head is entangled with the rest of the universe and I don't want to include the rest of the universe in my wavefunction.
You want to know what the probability is to measure your brain in a state where, say, your neurons are in a state such that you have lifelike memories of being raised by a wolf and then abducted by aliens. Well let's say your head fits in $1 m^3$ of space. Then the space of all possible configurations has a volume: $$1 m^{6\times 10^{23}}$$
(Not meters cubed/meters to the third power! Meters to the six times ten to the twenty three)
First, to be clear about something, let me go through an example with a dartboard first. What is the probability of hitting the spot $0.5$ meters from the left of the dartboard if you throw a dart that lands somewhere between $0$ and $1$ meters from the left of the dartboard? Well, the probability to hit that exact point is zero. If your dart throws happen to be uniformly distributed, then the probability of throwing a dart within an interval of length $x$, is $x$. You need some parameter $x$ depending on how specific you want to be. I'm going to do the same thing below, with an $x$ that depends on how specific you want to be.
Denote that big number $6\times 10^{23}$ by $y$.
If you want to know the probability of you having that memory, plus or minus a few memories (that's where $x$ comes in), you need to divide the volume in phase space of having that memory: $x^{y}\mathrm{m}^y$, by the total volume in phase space the brain can occupy, $1 \mathrm{m}^y$. This tells you that the probability of having a state with those memories is somewhere around
$$x^{10^{24}}$$
where $x$ is any number you like. It could be $.9$ for all I care. You still get a probability on the order of:
$$10^{-10^{24}}$$
For reference, there are about $10^{8\times 10}\approx 10^{10^2}$ atoms in the observable universe.
