1/ Right to say it's not possible to predict 100% what courts would do - but, remember Miller 1 and 2 were both in essence strong restatements of principle of parliamentary sovereignty. Padfield principle (executive can't frustrate purpose of legislation) is founded on that
2/ If you just look at Padfield itself (50 yrs+ old and principle developed since) you can see how difficult it will be for govt to argue a side letter contradicting the letter required by Benn Act would be a lawful use powers/within powers of minister bailii.org/uk/cases/UKHL/… 
3/ And since then we have had Miller 1 and Miller 2, both very strongly based on principle of parliamentary sovereignty, and the most basic currency of that principle is that Parliament can pass laws which set the lawful boundaries of ministers' actions - see para 41 of Miller 2
4/ Govt could argue a complex matter of international treaty negotiation and it has prerogative power outside boundaries of Benn Act to negotiate. But since Benn Act's purpose clearly to force govt to seek extension, hard to see actions frustrating that purpose could be lawful
