Yes and no, depending on how your GM plays Inquisitors (and what fluff they hold above others). While they technically could search your mansion-cabin or interrogate you on suspicion, as a Rogue Trader you are Peer of the Imperium. Which means you have a certain social "benefit of doubt". You also (unless you've alienated everyone) have powerful friends to can insure your discomfort and inconvenience is known to several other members of the Inquisition.
A simple search, perhaps, nobodys going to do anything about, but anything serious against a Peer will draw the attention of Hereticus Inquisitors who watch their fellow inquisitors for just such an abuse of authority. If the offending Inquisitor is unable to provide some kind of reasonable justification (and particularly if they have a history of these kinds of things) they may find themselves under investigation for potential corruption.
Of course, for people who aren't Peers (say, officers and below), it would take a lot more to get someone concerned. And once your down to Ratings and the like, well, they're guilty until proven innocent.