Yes, you can represent them in a DAG.
In the structural framework, the DAG is nothing but a visual representation of the functional arguments that enter the structural equations. For a quick review see the appendix of the Crash Course in Good and Bad controls.
As an example, consider the following structural causal model:
$$
\begin{align}
X &= f_x(U_x)\\
T &= f_t(X, U_t)\\
Y &= f_y(T, X, U_y)
\end{align}
$$
Where here the disturbances $U$ are mutually independent (this assumption is not necessary, and just for illustration purposes).
The model above has an associated DAG:
Where independent disturbances are usually omitted for clarity (they need not be).
Now let us represent the potential outcomes in a DAG.
Note the potential outcome $Y(1)$ is defined as the solution to the structural equations when we set $T=1$.
$$
Y(1) = f_y(1, X, U_y)
$$
Note the only parents of $Y(1)$ are $X$ and $U_y$. You can thus write the DAG of the variables $T$, $X$ and $Y(1)$ as:
In this DAG you can read that $Y(1) \perp\!\!\!\perp T \mid X$. The above logic is general, and with that you can write as many potential outcomes as you would like in your DAGs.
For instance, using the same logic, you can derive $Y(0) = f_y(0, X, U_y)$, and if you want to, you can represent both potential outcomes in the same DAG:
Where here we now do need to write the disturbance $U_y$, since it is common parent of $Y(1)$ and $Y(0)$.
This allows you to read the joint independence $\{Y(1), Y(0)\} \perp\!\!\!\perp T \mid X$.
