I say no, and for entirely practical reasons.
The step which, from my point of view, you are failing to make is to actually go look at how consciousness is created and ask, "Is this a function that can be maintained by something that works as slowly as a pencil brain?"
I say no, because you don't have simultaneous coordination of large enough amounts of coherent data over short enough continuous spans of time to achieve it.
That's why I say that the pencil brain cannot mimic that particular function.
I am addressing this point.
This next part isn't going to convince you, but just let me say it first.
The smallest possible unit of time is Planck time, on the order of 5*10^-44 seconds. Rather brief. Nothing happens that is shorter than that duration. If we looked at your brain using that time frame, you would no longer talk about 'simultaneous coordination'. Events that are happening simultaneously are in fact happening glacially - you wouldn't even see things happening on that time scale. The impulses running from neuron to neuron in the chemical soup would appear absolutely frozen to you on that time scale. you'd have to leave markers and come back days later to even notice they moved. You could reach in 'by hand' on that time scale and make things happen, one at a time, one neuron at a time, and have time to play a golf game and go to the symphony between each adjustment. Heck, at that time scale, you could write a million novels between each look at a single neuron (there are only 100 billion to concern yourself with, after all). In other words, at that time scale, even though things are happening simultaneously, the signals and events are happening so slowly that there is no need for changes to happen simultaneously - you can easily do it one at a time. You wouldn't be talking about simultaneous on this time scale, you certainly wouldn't be talking about continuous. You'd see an absolutely frozen object that appears to do nothing over 100 years. This is unarguable - on a given time scale, that actually exists in our universe, the brain is basically doing nothing, 'continuous' has no meaning, and yet it produces consciousness. Hence, continuous is not a necessary property of consciousness.
Okay, so at this point I'm assuming you aren't convinced. If not, you are positing something 'special' about simultaneousness that creates consciousness. From a computational point of view there is no reason to assume that. Certainly there is a need for our neurons, running at the speeds they do, to be simultaneously doing things to get everything they need to get done in the time they have available. But if those neurons were running, say, 10 trillion times faster than they do right now, why couldn't you just have one trillion, and a big bank of memory do all the work of your 100 billion neurons? Computationally, they are equivalent, and I think we now have you say consciousness is computational. Again, this is a thought experiment, no need to point out that our neurotransmitters wouldn't work at that speed.
I'm not sure what you meant by 'practical'. Certainly with our brain we need parallel processing to get things done in time. But the pencil brain is not constrained by our time scale, where 10^-44 sec is too small to notice, and 1 is a small, but noticble time increment. With the pencil brain, I'm saying 1 second is it's planck time interval. Unable to perceive it, basically nothing happens during it, the brain is frozen. But as 10^44 seconds passes, the pencil brain will perceive, it will think, it will be conscious. They are computationally equivalent.
I assume that you don't think the neurotransmitters are creating a 'field' or something that creates consciousness. I think we are both on the same page - it's how large bundles of neurons process information, self-referentially, that creates consciousness. It's the processing, nothing more. If so, there is no fundamental difference between parallel and sequential processing. Again, back to the planck scale. Sure, even at that speed, there's an impulse running along nerve 10234 and another impulse along nerve 2343322. Simultaneously! Sure, but it's not the impulse thats creating consciousness, it's what happens when it reaches the neuron (broadly). A neuron gets a bunch of inputs, and at a certain threshhold it fires. At the scale of Planck, it'd be an astonishing miracle if two neurons got a signal at the same moment. At that time scale (if you were living such that a planck interval felt like one second to you) you might wait decades between two events you swear are instantaneous. So, we know simultaneous in that sense plays no role.
So, we are left with the field concept. I don't see any evidence for such a thing, so I dismiss it. If there was a field, then speed and simultaneousness could matter, and the pencil brain, running on a substrate that doesn't generate that field, wouldn't work. But, that is just pie-in-the-sky speculation.
I can't think of any other objections or alternatives. In a time scale that actually exists on this world, your brain does not do the 'important things' simultaneously or continuously. Where 'important things' mean neurons receiveing impulses and firing. It's the receiving, firing, and storing data that creates the consciousness, not the mere fact of neurotransmitters propagating a signal.
Therefore, a pencil brain operating on a time scale of seconds would work too, and would perceive time passing in parcels of billions of eons.