Will a shift in the average total cost curve mean that the marginal cost curve will also shift up?
No, a shift in the average total cost curve does not necessarily mean that the marginal cost curve will also shift up.

Your intuition is correct. Here is a simple numerical example:

Consider a shift from the total cost function $C_1(q)=q$ to $C_2(q)=1+q$.

Then the average cost functions shifts upward from $AC_1(q)=1$ to $AC_2(q)=1/q+1$.

But the marginal cost function which was $MC_1(q)=1$ remains unchanged at $MC_2(q)=1$.