International treaties do not have force of law. The actual statute that has force of law in the relevant jurusdiction, i.e. the U.K. where the U.K. police would be acting, is The Diplomatic Privileges Act 1964.
This imports parts of the Vienna Convention into law, the parts that are explicitly given in the schedule to the Act, and makes several modifications (mostly translating terms from terminology used in the Convention to terminology used in U.K. law) and additions along the way.
The most interesting additions here are:
- the idea that the Sovereign can, by dint of an Order In Council laid before Parliament, withdraw immunities and privileges as xe sees proper from "such persons as connected with" the diplomatic mission, as stated in § 3 of the Act; and
- the idea that the Secretary of State gets to provide conclusive evidence for settling any questions of whether someone is entitled to privileges, as stated in § 4 of the Act.
So whilst Ecuador could assign Assange courier status, the U.K. could, under its own law, in response (or even proactively) determine that that was not "proper", promptly have an Order In Council declaring the privileged courier status withdrawn, and have the Secretary Of State conclusively certify that loss of courier status.
This is not a violation of the law. It is not even a violation of the terms of the convention, which does not require that any choice of couriers be allowed by receiving states any more than it requires that receiving states allow any choice of heads of missions.
To put it another way: The law grants privileges to diplomatic couriers, but it does not guarantee that anyone at all can get diplomatic courier status. ad hoc is not ad libitum.
Indeed, although it had not been abused enough by the time of the 1961 Convention for states to consider it worthwhile explicitly laying out that the rules about personae non gratae could be applied to diplomatic couriers, even though it was generally considered that they could, later draft articles from the International Law Commission explicitly dealt with this subject, clearly supporting the notion that the U.K. can follow U.K. law in this way and proactively or immediately deny Assange diplomatic courier status. These articles were instigated precisely because some states were seeing diplomatic bags and diplomatic courier statuses being abused.
Here are Article 11 and Article 12 of a 1989 set of articles drafted by the International Law Commission, addressing this point and clearly indicating the way that the wind blows on this issue:
Article 11. End of the functions of the diplomatic courier
The functions of the diplomatic courier come to an end, inter alia, upon:
(c) notification by the receiving State to the sending State that, in accordance with paragraph 2 of article 12, it ceases to recognize him as a diplomatic courier.
Article 12. The diplomatic courier declared persona non grata or not acceptable
1. The receiving State may, at any time and without having to explain its decision, notify the sending State that the diplomatic courier is persona non grata or not acceptable. […]
Observe that that very same text from article 12 is article 9 of the 1961 Vienna Convention.
It is not just "some mail", either. It is a diplomatic bag, which is a communication of a particular nature. Its nature raises another political consideration that militates against this idea: It would not be politically astute of Ecuador to entrust state secret communications to someone known for the practice of leaking them.