What is the shortcoming/pitfall of using the same antigen preparation for both mice immunization and ELISA/T-cell stimulation assessments, if any?
One pitfall occurs if the antigen preparation is not highly pure or contains contaminants that are significantly antigenic when compared to the antigen of interest. These problems are easily exacerbated with a strong adjuvant. The animal will raise a response to all of the antigenic proteins in the preparation, and if you coat ELISA plates with that preparation, you will be measuring the sum response to all of those antigens rather than just the one you are interested. This could lead to misinterpretation of the data such as an overestimation of the response to your antigen of interest.
However, people often have impure antigens or uncertain as to whether the 1% of contaminants in a 99% pure preparation has some highly antigenic components. So if you can have an irrelevant protein control for coating or for stimulation, or perhaps a "mock preparation", that is prepared exactly the same way as your antigen prep, you can subtract out that background from the signal of your antigen prep, or at least observe what the signal to the contaminants might be compared to a no stimulation or diluent stimulation well. There can be some caveats to this approach, but it's better than just comparing your response to a non-immune animal, even though people often do that.