Should have, but she didn't. This fact is noted too by the Inquisitor in their report.

When the authorization to bring Leia Organa in for questioning is granted, therefore, it's two Inquisitors, not just one, that show up at her office in the Senate. They have a squad of troopers and full access to the security systems, and two more Inquisitors with their own troopers covering exit routes.

The Alderaan Senator's office door is not so much "knocked on" as it is "knocked off its hinges".

The Empire would know if she wasn't there, of course. Would almost certainly notice a convincing body double - there's reasons to send Inquisitors beyond countering Force powers. Would likely notice clever manipulation of video feeds. 

So Senator Leia Organa sits behind her desk like nothing is wrong, her staff having already gone home for the day while she works as late as usual. She stands when the door flies in, expression stern. "What is the meaning of this?" she demands. 

The Inquisitors' uniforms are designed to obfuscate the body as much as possible and the masks are blank and faceless. It might then be difficult to tell which one of one of them says, voice harsh and buzzing through the filters, "Leia Organa, you are being detained under suspicion of treason. Place your hands on your head and turn to face the wall."

She does as ordered, demanding still - "What exact accusations do I face?"

"We don't have to tell you that, your highness." That's definitely mocking sarcasm. Also the sound of shockcuffs warming up.

"I have rights as a sitting Senator."

She doesn't move. 

Snrk. "That's adorable." Leia's arms are roughly pulled down and cuffed behind her back. "Come on, princess, let's go."

She keeps her chin high as they march her out, her stride stately and unhurried, like they're simply escorting her. "The body of the Senate will not stand for such treatment of one of their own," she warns, sternly. 

"And maybe if we answered to the Senate, that'd be worrying."

She goes quiet.

Yeah, that's right. Not so tough once the illusion of your flimsiplast 'laws' is stripped away, huh? They'll soon see how she faces up to real power.

She remembers to complain, with oddly well-tailored comments, whenever they're in earshot of anyone else. (Especially anyone else who might discover an uncomfortable rebel sentiment at witnessing this.)

Her guards are doing their best to scare off anyone inclined to stop and observe. And there are enough of them that most people don't get very close.

She can protest her innocence both very loudly and very efficiently! 

News of her arrest will make the gossip circles then, at least, even if it's likely to get the usually ruthless suppression treatment with the actual news media.

The gossip circles are her goal right now - the Senators wondering who would stand for them if they're led off on trumped up charges. The Senators who will try to lodge a performative objection, and get nowhere or worse, who will question how much power they really have. The Senators who will look at the erosion of the few rights they cling to as elites, they alone in a galaxy stripped of all dignity, and will wonder if, maybe, just maybe, they've made a mistake in collaborating with the Empire. 

The aides Leia has carefully cultivated fond and admiring impressions with. Any who remember what Alderaan stands for.

Any who might weaken for just a moment, just long enough for treasonous sentiment to drip into their ear. 

That doesn't show in her face, pisture, or muted presence in the Force as she's led to whatever awaits accused traitors. 

In this case, that would be a speeder to the Inquisitorial headquarters. The ride doesn't take long; that building, like the Imperial palace, are in the same district as the Senate tower. Before she's let out of the speeder, a bag is thrown over her head, blocking her view. As she's bundled along, she may infer that her final destination is fairly deeply nested- the route involves two separate turbolifts.

The bag doesn't do much to her ability to walk confidently, with measured steps (nor to track where she's going).

Then maybe she'll be able to find her way back out when they reach their destination and the bag is removed from her head. Said destination being a small cell, into which she is summarily shoved after the cuffs are removed as well.

The door slams shut behind her.

She surveys her cell like a queen surveying her castle, then turns, and sits on the bench, and waits.

The cell contains:
-A bench set into the wall that has a slightly softer surface than the rest of the floor and walls
-An overhead light which buzzes quietly to itself in an irregular pattern and flickers twice in the first thirty seconds of her occupancy
-A pop-out toilet
-And that's it

They seem content to let her sit and stew for the next six hours.

After hour five she gets up to knock on the door.

This has no discernible effect beyond making a little noise.

She frowns at it, then settles back again to wait.