You have asked a very interesting question and I am afraid the answer is yes and no! I will try to explain it as best I can.
Braces CAN change profiles:
Braces can change profiles only when the orthodontists and the patient plan to get it changed from the START of the treatment. A good example is when patients complain that when taking photographs, they notice that their side profile is sticking out and they have a very full smile (most patients use the terms, I look like a horse!). In this case, braces can help to retract the teeth to allow the patient to have a softer, gentler profile.
Braces CANNOT change profile:
Some patients worry that braces may damage their profile. If you have a nice profile and only want your teeth straightened, then the orthodontist will plan the treatment so that braces will not alter your profile. However, if treatment is not planned properly, especially in cases of teeth extractions, braces may actually cause your profile to flatten.
Orthodontic treatment restricts the movement of teeth within the jaw bone. It is unlikely that braces itself will ‘make’ the chin more V-shaped. However, it is more likely that the illusion of straighter teeth, more confident smile and better profile creates the slimmer illusion on the face. Patients tend to lose some weight during braces treatment so this may help with that too!
The mild crossbite you mentioned will depend on where the crossbite is. Is it at the front or back? Does it include one or multiple teeth? Does your chin slide to one side? Therefore assessment of the crossbite is crucial before answering your question on whether it will change your profile.