Google Experiments supports first click attribution, last click attribution, and even data-driven attribution. To specifically answer your question, will the variant that the user first saw get credit for the transaction or not depends on the attribution model selected .If the first click attribution model is used, the variant that the user initially saw during the experiment is likely to receive credit for the transaction.
However, it's important to note that Google Experiments allows you to define custom conversion goals and configure the attribution model within Google Analytics.