I spent some time learning FEMM to figure this out.
The answer is yes, the case does make a notable difference in the pull on your plunger.
Without a case the pull on my sample plunger was 0.036 N
And with a case the pull was 0.047 N
Edit: Playing with the simulations more, the effects of the case are more drastic as the plunger moves into the cavity. As the plunger approaches the other side, you'll start seeing at least an order of magnitude of difference, so not only is itthe case important but it is very important.