It can - basically, redefine the kernel $k$ as follows:
$$
k = \left[ \begin{array}{} 1 & 1 & 1 \\ 1 & 9 & 1 \\ 1 & 1 & 1 \end{array} \right]
$$
Then redefine $f$ as
$$
f(u) = \begin{cases}
1 & \text{if } u \in \{3, 11, 12\} \\
0 & \text{else} 
\end{cases}
$$
This corresponds to the previous parameterization via $(0,3)\to 3$, $(1,2)\to 11$, $(1,3)\to 12$. Now the system can be written simply as $u_{t+1} = f \circ (k * u_t)$. 

This works because the value of 9 in the center cell outweighs the sum of its neighbors, so $k*u_t(x)\geq9$ guarantees $u_t(x)=1$, and likewise $k*u_t(x)<9$ guarantees $u_t(x)=0$, with $k*u_t(x)\bmod 9$ being the neighbor count.

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Some comments: I began thinking about this after trying to implement Game of Life on this cool web app called [neuralpatterns.io](https://neuralpatterns.io) which only supports scalar reaction-diffusion systems. It suggests a family of similar systems with sharply mean-centric dispersion kernels and bimodal activation functions which display Life-like dynamics. Also, the scalar form is that of the somewhat obscure [integro-difference equation](https://en.wikipedia.org/wiki/Integrodifference_equation).