Yes, one mesh cells is enough for structures that do not change along the direction of propagation. The cell purpose is to calculate the mode profile that will be propagated over a certain distance. Since the mode profile does not change over the length of our discussed cell, we do not need to include more cells. This is also one of the big advantages of EME.
This behaviour is nicely shown in the following picture that is taken from the MMI example on Knowledge Base:
You can notice that the tapers that vary their profile in the direction of propagation are resolved with multiple cells, but the main bulk that has constant profile can be resolved using only one cell.
I believe that the field distribution resolution you mention in your post is related to the monitor resolution settings. You can actually set the resolution in x direction in the field profile monitor properties as it is shown in this KX post.
Here is a comparison of the above mentioned MMI example between monitor with x resolution of 10 and 1000 points: