A will has no effect at all until it has been validated by a court (= 'probate registry'), giving the executors power to distribute the testator's estate. That's what probate is, so of course it's essential.
However I note that your question refers to 'a property' (rather than just 'property'), so I assume that a house is involved here. If a house is owned by a husband and wife (or, indeed, by any other two people) as 'joint tenants' then it's their 'legal partnership' which owns the whole house, rather than them each owning half of the property (as they would if they owned it as 'tenants in common'). In the event of the death of one of them, the other person (as the surviving member of the partnership) automatically owns the whole house, with no need for probate in respect of the transfer of its title. That applies whether there's a will or not.