Will t-butoxide still form less substituted alkene when there is a possiblity for more stabilisation?

Consider this reaction:


[![enter image description here](https://i.stack.imgur.com/Rd3xv.png)](https://i.stack.imgur.com/Rd3xv.png)


Will a usual Hoffman elimination take place or will a carbocation form by leaving of $\ce{Br}$ and rearrange to give a conjugated alkene like this one:


[![enter image description here](https://i.stack.imgur.com/2Fn6u.png)](https://i.stack.imgur.com/2Fn6u.png)


I have heard that reactions with t-Butoxide are E2 and hence carbocation are not formed. So wouldnt the major product still be the least substituted alkene?


