Answer:
No. It is illegal to have a platypus as a pet, and you would not be able to provide the conditions it needs. It would die very quickly as platypuses are highly sensitive to ecological changes. Platypuses are native Australian animals, and therefore protected by law. They are not permitted to be kept as pets in Australia or any other country.
There are very few zoos overseas permitted to keep platypuses, and only a limited number of facilities in Australia keep them for either display or research purposes.