Applying air barriers and insulation to the exterior of an existing building is going to change the thermal and moisture performance.
IMPORTANT CONSIDERATIONS:
DRYING POTENTIAL INSIDE AND OUT - Allow for materials to dry toward the interior AND the exterior. An airtight layer on the exterior may trap moisture from the interior.
MOISTURE PERFORMANCE - A material applied to the exterior is going to get wet. Plan for durable layers that shed moisture easily.
FIRE RESISTANCE - Plan for materials that resist the spread of fire and/or have a multi-hour fire rating.
DURABILITY - Plan for materials that will last for the life of the building (or longer!) and think about the recyclability or reuse.
The object of making a building airtight is to prevent air leakage and moisture transfer into assemblies. Adding extra insulation is easy to do on the exterior.