it possible for the machine to rust inside the boiler at the base? And if so, should I take it apart to try and remove it?

No this is just exposed copper/brass, as Pat mentioned before, i'd just leave it as it is. no need for further descaling, disassebling etc. I would recommend using RPavlis water (100mg sodium/potassium bicarbonate per 1l of distilled water) to prevent scale buildup in the future and also protect your copper heating element.
cheers,
Rob