Han formerly being a part of the Imperial military has long been part of the extended universe of Star Wars. With the release of Solo: A Star Wars Story, it was established in Disney canon that Solo deserted from the Imperial Army while he was assigned to Minban. In that film, it is even mentioned that hunting down a single deserter is not a priority for the Empire, but that doesn't mean that they never do it or would not take action if they happened to cross paths with a deserter.
In Disney canon, does Han ever face any particular repercussions after his escape from Minban from his status as a deserter? He is captured by the Empire at least twice later in his life (on Bespin and the moon of Endor), but I don't recall any particular mention of any specific punishment for desertion or even any hint that the Imperial forces there even recognize that he is a deserter or consider him anything other than "Rebel Scum" and (on Bespin) someone with a bounty on him by Jabba the Hutt.